How did Saruman know who Gimli was ?

[Pitchwife]

I suppose Wormtongue told him, though it's not quite clear how Wormie knew who Gimli's father was. When Gandalf introduced his companions on their arrival in Edoras, he only referred to Gimli as 'Gimli the Dwarf'. But Gimli himself gave his full name to Éomer when they first met (in The Riders of Rohan), and Éomer may have mentioned it when he reported to the King (presumably in Wormtongue's presence).
(I don't think the Palantir had anything to do with it - unless you suppose its user interface included little pop-ups providing names and biographical information on people seen in the stone when you thought-clicked on them.)

[Legate of Amon Lanc]

Personally, I would think it was only the fact that Saruman encountered them by the Fangorn forest, and then, the news Wormtongue brought. Gandalf says something about Aragorn, later, to Pippin, and I think we can apply a similar pattern to Gimli:

Originally Posted by TT, Palantír

It may be that [Sauron] will learn that I was there and stood upon the stairs of Orthanc-with hobbits at my tail. Or that an heir of Elendil lives and stood beside me. If Wormtongue was not deceived by the armour of Rohan, he would remember Aragorn and the title that he claimed.

[Aaron]

Gimli was a courageous, hardened warrior. Perhaps tales of him and his lineage reached Isengard?

[Inziladun]

Originally Posted by Aaron

Gimli was a courageous, hardened warrior. Perhaps tales of him and his lineage reached Isengard?

Courageous he certainly was. However, I think he would have been of absolutely no interest to Saruman were it not for his involvement with the Company of the Ring.

[Legate of Amon Lanc]

Originally Posted by Inziladun

Courageous he certainly was. However, I think he would have been of absolutely no interest to Saruman were it not for his involvement with the Company of the Ring.

Exactly. With all respect to Gimli, son of Glóin, I am pretty sure Saruman's attitude would be "Dwarves? These funny little ground-diggers? Does that even exist still?" (Funny, by the way, imagining that from former Maia of Aulë. But I could indeed think it was like that.)
Judging from Saruman's speech to Gandalf:

The Elder Days are gone. The Middle Days are passing. The Younger Days are beginning. The time of the Elves is over, but our time is at hand: the world of Men, which we must rule.

I think for Saruman the Elves were done for, but the Dwarves were never even worth mentioning. I mean, really. Try to think like Saruman: he would look at the achievements in Middle-Earth purely from the basic look at the timeline. Who was in Saruman's eyes "cool"? Likely some great Elven kings of old, who had the power to overthrow Morgoth or Sauron (although most of them still died, losers them). Dwarves never really made a big difference, not in the way noticeable by Saruman. The only thing they would be useful for, if you asked, would have been probably mining gold, so that you could make nice rings out of it. And that's probably all.

So all in all, no. Gimli son of Glóin was familiar to Saruman because he happened to be a member of the Fellowship. Hm, speaking of this, I think I know - if Saruman had spies (birds and such), they probably told him how many people are in the Company and who they are, and of course he would then search for who exactly they might be. And the journey of Gimli and Glóin to the Council would have been easy to track for his agents, most likely.

[CSteefel]

It is a bit hard to imagine that Saruman's animal spies were able to pick up that the dwarf's name was Gimli and that he was son of Gloin. Even the night time visit to the the campfire would not have given him this information.

Only one I can think of is Wormtongue, who would presumably have heard the name from Eomer or one of his men, since this is where Gimli announces that he is Gloin's son. Since Eomer lent them the horses, and the guards at the gates of Edoras knew that they were returning with those horses (as Gandalf notes upon arrival), the names of the three wanderers who they had met to the north would be known to Wormtongue...

[Inziladun]

Originally Posted by CSteefel

Only one I can think of is Wormtongue, who would presumably have heard the name from Eomer or one of his men, since this is where Gimli announces that he is Gloin's son. Since Eomer lent them the horses, and the guards at the gates of Edoras knew that they were returning with those horses (as Gandalf notes upon arrival), the names of the three wanderers who they had met to the north would be known to Wormtongue...

Now that I think about it, that's probably the most likely. Éomer did indeed hear Gimli say he was the son of Glóin at their first meeting, and that was the only time Gimli's father is mentioned in that part of the book. At the time Aragorn, Legolas, and Gimli see the old man at the edge of the trees, only Gimli's name had been said when the old man was likely to have been watching.

[Elmo]

Originally Posted by Pitchwife

I suppose Wormtongue told him, though it's not quite clear how Wormie knew who Gimli's father was. When Gandalf introduced his companions on their arrival in Edoras, he only referred to Gimli as 'Gimli the Dwarf'. But Gimli himself gave his full name to Éomer when they first met (in The Riders of Rohan), and Éomer may have mentioned it when he reported to the King (presumably in Wormtongue's presence).
(I don't think the Palantir had anything to do with it - unless you suppose its user interface included little pop-ups providing names and biographical information on people seen in the stone when you thought-clicked on them.)

I'm not 100% but I don't think a palantir has a sound card installed so you can't hear anything with it so he can't have heard Gimli son of Gloin being spoken with it.

[PrinceOfTheHalflings]

Saruman didn't spend all his time in Isengard. We know he visited Minas Tirith and he was part of the White Council ... so he must have attended the meetings. We also know that he participated in the attack on Dol Guldur, so he got around a bit.

I wonder if he'd ever visited Rivendell? Elrond would have had no reason to turn him away.

What I'm saying is - he probably knew of more people than we think! Remember, he was interested in the One Ring ... Bilbo found the Ring and Gloin was one of his companions... it's not inconceivable that Saruman knew something of this, given his interest.

[Inziladun]

Originally Posted by PrinceOfTheHalflings

What I'm saying is - he probably knew of more people than we think! Remember, he was interested in the One Ring ... Bilbo found the Ring and Gloin was one of his companions... it's not inconceivable that Saruman knew something of this, given his interest.

I do think it likely that Saruman knew Gandalf had a plan to eliminate Smaug, but I doubt he knew the details. If he'd been aware Gandalf was leading thirteen Dwarves and a Hobbit to the Lonely Mountain to destroy a dragon, his likely conclusion would have been that old Olórin had finally gone off the deep end.
Saruman probably didn't pay too much attention to Thorin and Company at that time, since he was occupied with getting Sauron out of Dol Guldur. I wouldn't think the names of the Dwarves involved would have been something he would have taken the trouble to learn.

[Legate of Amon Lanc]

I second Inzil. Also, apart from that, Bilbo's connection to the Ring was unknown to Saruman basically until the very end, when he got straight to the source - i.e. Gandalf, whom he imprisoned in Orthanc. If he would be interested in learning how did the Ring end up in Bilbo's possession, it would have had to be solved then, and again, we are basically around the same time there. Anyway, learning the Dwarves' names would have been of little importance to Saruman. I mean, Balin, Dwalin, Fili, Kili, Dori, Nori, Ori, Oin, Gloin, Bifur, Bofur, Bombur and Thorin would sound as funny to Saruman as they do to a reader of the Hobbit, except maybe for Thorin who was of some renown, but as good as dead (well, rather dead, actually). These names were of no use to Saruman as they didn't have anything to do with the Ring, and like I said above, at the time when Saruman could have learned about their connection to Bilbo, his immediate concern would be to get the Ring itself, which was somewhere in Eriador being chased around by the Black Riders.

AT MOST, though highly unlikely, Saruman could have - out of interest, or rather out of the pedantic obsession to know everything about the Rings - "googled" the names of the thirteen Dwarves around the time of Gandalf's imprisonment in Orthanc, which could have coincided interestingly with Gimli and Glóin's journey from Erebor to Rivendell, and maybe then Gimli's appearance in the Fellowship might have been more of notice to him, as he would get the feeling that "something is going on here" as the recurring characters revolving around the Ring appear. But personally I somewhat doubt that.

[PrinceOfTheHalflings]

Originally Posted by Legate of Amon Lanc

I second Inzil. Also, apart from that, Bilbo's connection to the Ring was unknown to Saruman basically until the very end, when he got straight to the source - i.e. Gandalf, whom he imprisoned in Orthanc. If he would be interested in learning how did the Ring end up in Bilbo's possession, it would have had to be solved then, and again, we are basically around the same time there.

That was the time I was thinking of. Of course Saruman wouldn't have been interested in the Erebor Quest back when the White Council were considering how to drive Sauron from Dol Guldur.

However, while Saruman had Gandalf in Orthanc, the Nazgul showed up (according to Unfinished Tales) looking for The Shire and a hobbit called Baggins. Saruman's spies in the shire would soon be able to tell him that there were two Baggins; Bilbo who had gone off into the wild on a quest with Gandalf and some dwarves and then disappeared mysteriously at his 111th birthday party and Frodo, who had inherited Bilbo's house and who had also mysteriously disappeared.

Once Saruman worked out that Gandalf seemed to be "behind" all this I'm sure that the composition of the Fellowship would have been of some interest to him. Especially as the Fellowship included Gandalf, Aragorn (Isildur's heir) and Boromir of Minas Tirith (whom Saruman probably met at some point in the past).

I don't think that Tolkien made a mistake here, I'm sure he intended that Saruman had done his homework.

[CSteefel]

I don't recall any mention of Gimli in the Hobbit, so how would Gloin's son have come to Saruman's attention through the business of Smaug. I also don't see what it would have to do with visits to Rivendell, since the visit of Gimli here also appeared to be a first for him.

There is a slight chance he knew of Gloin's name (although still unlikely that he would have focused on one of this large party of dwarves), but I don't see how this gets him the name of Gimli and that Gimli is Gloin's son...

[Rumil]

Agree that Saruman probably heard of Gimli via Wormtongue.

However I'd guess that he had some interest in the Dwarves of the Lonely Mountain. After all the Battle of Five Armies was a really major event that altered the balance of power somewhat. I think Saruman would have been rather fascinated as to how the Grey Wanderer somehow managed to arrange the demise of Smaug the Magnificent.

More importantly, putting 2 and 2 together, Balin's occupation of Moria might have made him sit up and take notice. Saruman was the expert on Rings of Power, I bet he had figured out that there was still one of the seven unaccounted for, though I'm not sure if Gandalf let on that it was taken in Dol Guldur? If not, then Saruman would have loved to get his hands on it and Moria wasn't too far for his spies to travel, or to do a bit of Palantir-ing.

Gimli was probably one of the top few dozen Dwarves of Erebor (in terms of social status) and Saruman, being the political operator we know he was, might well have complied information on the top players amongst the major powers of the time.