There are dozens of Greek first names still in use today.. Many of them don't sound so strange to us because we're familiar with them. It's usually only the names that are not commonly given to people nowadays or the ones that stem from Greek literature or mythology that make us wonder.
At the root of the difference in nomenclature in modern Anglo-Saxon languages is how these names (and the texts they appear in) came to us. The Roman pantheon is almost an exact copy of the Greek pantheon (Zeus = Jupiter, etc.). So for most of the mythology we will indeed have Greek names that were Romanized, but we went back to the Greek names during Hellenism. By that time, the planets and the Galilean moons of Jupiter (like Io) had already been seen by telescope, and that's why they have Roman mythological names. Moons discovered after Hellenism usually have Greek names (for Jupiter, for example, Elara and Pasiphae).
Literary studies of many Greek works were deemed heretical by the Roman Catholic church, so there had not been any adaptation of the texts and characters into medieval vernacular. Homer's works, for example, became available in English only in 1581.
As for the Biblical name references you mentioned, Peter as a name only makes sense if you take the original text or speaker to be Greek:
"Petros" in Greek is a first name as well as the word for "rock". This wordplay only makes sense in Greek, as well as does the phrase "the gates of Hades", which was altered in the New English and other translations.