Perseus was not as important to the Romans as to the Greeks, but his name would be the same.
While his name didn't change several of the heroes such as Odysseus and Achilleus did have Roman names, Ulysses and Achilles, so it is not just the gods that the Romans changed the names.
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The Romans only changed the names of the gods, not the heroes. So Perseus' Roman name is still Perseus.
Perseus was said to be born in Argos. So back then surnames were not used. So to answer this I wold say his name is Perseus of Argos.
It is believed to be derived from the greek "pertho(περθω)" meaning "to destroy," and is interpreting as meaning "destroyer."
Andromeda.
Danaë