[Formendacil]

Originally Posted by Mugwump

Because of who Gimli's father was, I would still be greatly surprised if Saruman didn't already know him by sight. Conversely, Saruman's calling him by name at that time could easily have been to show off his knowledge. I'm sure he used the Palantir and his other spies to scope out as much information about Gandalf and his companions as possible.

I'm not denying Gimli wasn't a Dwarf of some consequence. Assuming Thorin Stonehelm was an only child, and assuming there are no other missing figures in the branches depicted in Appendix A III, Gimli was 4th in line to the Durinic throne, after Thorin III, Dwalin, and his father, Glóin. On this basis, Gimli may well have been known to Saruman by name.

But I wonder if you are overvaluing somewhat slightly the efficacy of the Palantír. Here is a bit of what Tolkien said in his essay, "The Palantíri" in Unfinished Tales:

Originally Posted by J.R.R. Tolkien

But controlled by the will of a skilled and strong surveyor, remoter things could be enlarged, brought as it were nearer and clearer, while their background was almost suppressed. Thus a man at a considerable distance might be seen as a tiny figure, half an inch high, difficult to pick out against a landscape or a concourse of other men; but concentration could enlarge and clarify the vision till he was seen in clear if reduced detail like a picture apparently a foot or more in height, and recognized if he was known to the surveyor. Great concentration might even enlarge some detail that interested the surveyor, so that it could be seen (for instance) if he had a ring on his hand.

But this 'concentration' was very tiring and might become exhausting. Consequently it was only undertaken when the information was urgently desired, and chance (aided by other information maybe) enabled the surveyor to pick out items (significant to him and his immediate concern) from the welter of the Stone's visions.

My point with this longish quote is that getting familiar with the likenesses of various Dwarf-lords would not have been a particularly easy task for Saruman, and I have doubts as to whether he would have wasted this much energy on Gimli--or even Glóin. Although powerful, the Gróinic line was but a cadet branch of the house of Durin--and, as I noted, Thorin III Stonehelm might not have been an only son--and Dwalin might not have been childless.

All this assumes, too, that the Orthanc-Stone would have reached Erebor, which is not a good assumption, in my books. Quoting again, Note 18 from the same essay:

Originally Posted by J.R.R. Tolkien

Marginal jottings associated with this note are partly illegible, but so much can be made out, that the remotre the poast the clearer the view, while for distant viewing there was a 'proper distance', varying with the Stones, at which distant objects were clearer. The greater palantíri could look much further than the lesser; for the lesser the 'proper distance' was of the order of five hundred miles, as between the Orthanc-stone and that of Anor. "Ithil was too near, but was largely used for [illegible words], not for personal contacts with Minas Anor.

500 miles--Isengard to Minas Tirith. Very roughly making distance calculations with my fingers on the map in my paperback copy of Unfinished Tales, Erebor was another two-thirds as far again. Even assuming a certain amount of over-run in distance being possible for a strong mind, I think it's safe to say that Erebor was far out of casual viewing range for Isengard, and even Rivendell was pushing it.

Of course, if there is anywhere in Middle-earth that, in the late 3rd Age, was still shrouded from the sight of the Stones, I would think it would be the refuge of Elrond, which was still unknown to casual travellers, and ruled by one of the Wise, who had the lore of Arnor in his library (as well as the Elven lore of Eregion). So when could Saruman have started picking up Gimli in the Palantír? I am personally of the opinion that he wouldn't have been following the Fellowship until Anduin--maybe not even until Fangorn or Edoras.

This does not mean, with all the foregoing, that Saruman couldn't put two and two together. Undoubtedly, he must have had a few spies in Dale and Erebor, and when he noticed/heard that a Dwarf had travelled from Rivendell with the Fellowship, I expect he would have been able to recall that the near-royal Lords Glóin and Gimli of the House of Durin had left Erebor for Rivendell, and it wouldn't take much of a genius to deduce that, of the two, it would be Gimli who had accompanied the Fellowship.

So... I agree the Palantír played a role in this recognition, but I would downplay the extent to which Saruman was utilising it for the general recognition of not-quite-key lords in realms very far from his own.