Gray, the ornithologist at the British Museum, was so sure of himself that he revised the scientific names on all of the specimens then in the museum -- and then removed the original labels from the specimens!   He thus removed any information (which at that time to him seemed irrelevant) about when and exactly where each had been collected -- thereby destroying any scientific value of the specimens for later generations!   Gray removed Darwin's labels and substituted his own.   Needless to say, Gray (unlike Darwin) had absolutely no clue about geographic variation of species and the importance of specimens for documenting it.

You can still see Darwin's specimens (with Gray's labels) in the ornithological collection of the British Museum, which is now located in a modern building in the village of Tring northwest of London.

The reason that we do not know the island from which each of Darwin's Galapagos finches came is not Gray's fault.   Darwin did not write that information on his labels!   It subsequently became apparent that this omission was a major lapse on Darwin's part.   Darwin himself realized the error.   He wrote in his introduction to the "Birds",

"I did not suspect this fact [that the species of finches occurred on different combinations of islands] until it was too late ... but from the collection made for Captain FitzRoy, I have been able in some small measure to rectify this omission".

Stephen Jay Gould, the best-selling author of many books on evolution during the 1970's through 1990's (not to be confused with John Gould, the ornithologist that Darwin knew!), has opined that Darwin had preconceptions about the distributions of species and hence failed to record data he felt was irrelevant; in contrast, Captain FitzRoy had no preconceptions about the distributions of birds and thus recorded the islands where his specimens were collected.   (One of SJG's own preconceptions is that scientists inevitably distort their data to make it conform to their culturally determined preconceptions!)   Perhaps SJG's interpretation is correct, but ...

FitzRoy, the captain, was a confirmed creationist (like almost everybody then), with no detectable scientific interests.   He presumably had his men collect some specimens of curiosities of natural history to have as souvenirs of the voyage ... and he presumably labeled them in the same spirit that you might add the place and date to a postcard.

Darwin, on the other hand, might be excused from failing to label his Galapagos specimens accurately.   After all, who in the world at that time would have guessed that the Galapagos (or any islands) might have different species on them?   Furthermore, he had just spent three years exploring the coasts of South America, which provided almost no examples of species with such remarkably limited distributions.   In addition, the Galapagos finches are not very eye-catching birds, and Darwin had lots of spectacular things to see at that moment -- giant tortoises, marine iguanas, volcanos ....

Nevertheless, it would not have taken much additional time or effort to record the islands on which he collected his specimens.   It is never a bad idea to record extra information, even seemingly irrelevant information, when it doesn't cost you any time or effort!

Furthermore, Darwin did quickly realize that the mockingbirds and the giant tortoises in the Galapagos differed from island to island.   Why didn't he suspect, or at least consider, the possibility that other birds might also differ?

Maybe it just took a few days for the enormity of this discovery to sink in ... and by then he had mixed up the specimens from some or most of the islands.   A comment in his popular book for general readers, "The Voyage of the Beagle", suggests that he discovered his oversight while he was still in the Galapagos or soon afterwards.

When he realized the error, it must have been one of the lowest points in his life (the death of his young daughter about 15 years later was worse).   As the Beagle sailed away from the Galapagos headed across the Pacific toward home, and the islands slipped below the horizon astern, Darwin watched one of the great opportunities of his voyage sink with them.   I hope Captain FitzRoy shared some of the ship's rum!