Good question, Mark! Thank you!
The It's a Wrap! Star Trek costumes come with up to four pieces of identification.
Firstly, on the Star Trek clothing items themselves, many Paramount costumes have sewn-in, rectangular, cloth tags, usually identified with the official logo of the Star Trek television series or feature film for which they were made, or perhaps a generic "Western Costumes" tag (as in Gulf & Western/Paramount). These labels have lines for several wearers, and the name(s) of these actors, extra or stunt people, plus often an episode number, are hand-lettered with a laundry marker. It's unlikely there is any more extensive and official surviving documentation than this. (The Christie's 40th anniversary auction, last year, did sell off some albums of wardrobe continuity Polaroids, if I recall correctly.)
However, many of the costumes also have a thin cardboard "luggage" tag (below), which lists any individual items that go together to make one costume. This costume tag would have been originally attached to the hanger, and when the item gets sold off, it gets placed into the envelope with the Certificate of Authenticity. (In fact, I didn't think to look for the Andorian tag until my Tellarite costume arrived with one. I checked the bottom of the Andorian's envelope - and there was the tag!)
Costume tags accompanying my eBay wins
There's also the online eBay description, a paragraph (usually) listing the most important appearances of the costume. While it's obvious that the Paramount and It's a Wrap! staff have put considerable effort into researching the costumes, many of which have hung on racks since the mid 70s, they do make mistakes and hasty assumptions, and that's where fans like Jörg (who posts all manner of errors and corrections to the Star Trek Auctions, Props & Costumes bbs), come in handy!
I actually lucked out on my Andorian costume, as the eBay description seems to focus on the costumes first onscreen usage, as per the costume ("luggage") tag. Had they used the sewn-in tags, they'd have listed the actor who first wore the outfit in scenes later reshot with a different actor, and the major re-use of the costume - with an additional cape - by a named character in a later episode! Had there been more information online, the price would have gone much higher!
Similarly, as I noted in my Tellarite post, the fat-suit's sewn-in tag (below) reveals that it has a more extensive life than the outer costume, and a quick Google search on actors' names, and/or episode numbers, brings up some exciting research results! It even revealed an extra name I could add to Memory Alpha.
The sewn-in tag reveals its history!
Finally, there's a Certificate of Authenticity from It's a Wrap! This features the title of the item, exactly as it was listed on eBay, and a small photograph of the item.
I recall Richard Arnold, then-Star Trek Archivist at Paramount, once mentioning the fun he had during the lead-up to 20th anniversary of Star Trek in 1986. A huge display was being organised and, for the first time, a serious rummage was made through the surviving costumes and props of the original series, the failed "Phase II" and the early movies. Much of TOS was unlabeled, but even more had been lost to the winds of time (or rejigged for renting out to shows like "Mork and Mindy"). At one point, someone found a box of random scarves. Richard suddenly recognized the colours and patterns, and realised it was actually a skimpy outfit once worn by one of "Mudd's Women"!