Did anyone know?

[Feanor of the Peredhil]

Perhaps the really bad guys...? In Return of the King, it cites a bunch of times that the Witchking was not ready to fight Gandalf, that Gandalf was great, and all of that, and it kind of makes me think that he might have a decent idea of just who Gandalf is. Which would mean that Sauron knows, but that's almost a given, since Saruman was being manipulated by Sauron, and that would probably mean Sauron's got a pretty good working knowledge of just who these guys are. Plus them helping to oust him from Dol Guldur.
Would Bombadil know? I'm not sure... I generally hate that you can't pin him down to anything. I don't think the Ents knew, because of how Fangorn referred to "young" Saruman. Just thoughts...

Fea

[Neithan]

None knew at that time whence they were, save Círdan of the Havens, and only to Elrond and to Galadriel did he reveal that they came over the Sea. ---from the Sil

Surely if they did not know where the Istari where from, then they did not know what they were.

[Boromir88]

Feanor, nice point about the Witch-King, a good possibility. I don't think there is anything that would show Bombadil knows about it.

Thanks for the quote neithan, it's definately helpful.

[Lalwendë]

There's always the possibility that those of the Noldor who returned to Beleriand knew of the Istari from the Undying Lands. I would imagine such figures would have been well known, or at least known of. There are hints that there were possibly more Istari, and characters such as Galadriel may have recognised their qualities in Gandalf and Saruman, even if she had never previously met them.

Sauron himself may have recognised them as he was on something of an equal footing, hierarchically speaking. The Istari may have travelled in the disguise of elderly men, but I don't doubt that Sauron would have been able to discern their true nature, if Cirdan could.

[obloquy]

Tolkien wrote somewhere that Glorfindel, after his death to Gothmog, while still recovering his spirit in Aman, became friends with Olorin.

[Neithan]

There's always the possibility that those of the Noldor who returned to Beleriand knew of the Istari from the Undying Lands. I would imagine such figures would have been well known, or at least known of.

If you are saying that the Istari were already a group in Valinor and would be recognized as a group, the my response is that they were not a previously existing group, the group was formed for the purpose. If you are saying that each Istar would be recognized individually then I would say that that is why they did not use their real names, and I doubt that anyone would recognize them in their old man form if they did not want to be recognized.

[Boromir88]

Tolkien wrote somewhere that Glorfindel, after his death to Gothmog, while still recovering his spirit in Aman, became friends with Olorin.

I speculated whether Glorfindel knew too. He definately learned a lot from his death, and I find him to be one of the more reliable sources in LOTR. I find his statements in the Council of Elrond, although speculation, to be rather accurate.