How did Saruman know who Gimli was ?

[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...