Why the name of "Odisseo" (Homero) was swapped for "Ulisses"?

Answer 1

Odysseus is the Roman name and Ulysses is the Greek name.

Answer 2

The previous responder ("dragonmom") got it backwards:

The hero of Homer's epic is named "Odysseus" in the original Greek, but (for reasons I don't understand), in the ancient Roman world he was referred to as "Ulysses."

Similarly, the Greeks and Romans had many of the same Deities, but they had different names. For example, the Greek Goddess Athena was called Minerva by the Romans.