Welcome! This is a good question, and the short answer is that the Greeks used both names, depending on the context.
"Hades" is the older name associated with this deity. Over time, of course, that word also came to be associated with the realm of the underworld itself1. (In classical Greek, unlike English, the grammar makes it clear whether you're talking about the god or the place.)
Eventually, we encounter the notion of "Pluto" in Greek literature. Here, you'll find it used, first, as a ritual title for Hades1. But more and more, the word "Hades" becomes primarily associated with the place, and the word "Pluto" emerges as a way to indicate a different "persona" of sorts from the ancient, long-established ideal of Hades. Pluto is not a separate figure from Hades; rather, Pluto is something of a different characterization of the same god2. (Basically, Pluto is a more positive, less rape-y version of Hades3.)
When the Romans borrowed these names in from Greek, they associated the word/name "Pluto" with the Roman god Dis Pater, and "Hades" with the Roman god Orcus. Some time afterwards, the Romans started using "Pluto" to also refer to their god of the underworld. This is where the common modern-day misconception comes from: people nowadays usually hear that "Pluto" is the Roman name for "Hades," but in reality, both names were originally Greek.
And that's just the start! There are many variants in usage over the centuries, and many cases of overlap. But as far as your particular question goes, the take-away here is that Romans and Greeks did not use the names in precisely the same ways2, but the Greeks did in fact use both names.
- Editor's notes, Oxford World's Classics edition of the Library
- See Hansen's Classical Mythology
- Compare the Library account with Ovid's descriptions of Persephone's abduction in Metamorphoses and the Fasti. (Ovid refers to him as Dis rather than Pluto, though.)