I'm a big fan of my own theory (
).
Tolkien heard the names in Elvish, which he understood the way many of his characters understood Elvish - by some osmosis intrinsic to Elvish.
On each return to our world, sans the osmosis, he had a terribly hard time remembering the actual words and names, though he had a joy of a time remembering the linguistic characteristics and meanings of the words and names. So he set himself a lifetime task recreating Elvish from its patterns.
He wanted the most linguistically authentic names he could devise, as well as the ones that would ring in the ear most similarly to his impressions of the originals. But since he knew that capturing the actual originals was hopeless, he didn't fret over his many scrapped attempts. Rather, he continued to be fascinated by the challenge.
Whether you prefer to believe that Tolkien visited ME in some reality, or in dreams or meditations or extremely vivid imagination, my working premise (because I think it's such a cool premise) is that he believed his impressions of ME were real, or real enough to warrant attempting to reproduce them "authentically," and he made a sharp distinction between things he tried to reproduce and things he knew he was making up for literary convenience.
Names he scrapped quickly can therefore be viewed as ones he found unsatisfactory, and those he kept longest as most satisfactory - but satisfying which criteria? Galadriel probably had to match a linguistic pattern of relating to both light and trees, but Gandalf had rather to suit its role as a folkname among hobbits. These are rather different criteria with different resolutions. And they lead to different questions:
In the ME that Tolkien experienced (by whichever route), did all speakers of the Common Speech really call Gandalf the same name? Or were there different nicknames in the Shire, in Rohan and in Dale, etc. Did Tolkien consciously decide, when he settled on Gandalf as the best stand-in for whatever the hobbits called him, that for simplicity's sake he should have all CS speakers call him that, too, even though he knew otherwise?
Can we suppose that Bladorthin (Gandalf in the early Hobbit drafts) was most satisfying linguistically, but that eventually Tolkien had to concede that it failed so utterly sociologically that he had no choice but to pick something out of our folklore to match the folkloric quality of Gandalf's true hobbit nickname?
I would assume "yes" to the last two questions, and I find many other interesting resolutions in light of this approach.