In the Hebrew scriptures Abraham's name is Avraham and not Abraham (אַבְרָהָם). Is has a v and not a b. The same goes for Rebecca, who is called Rivka in Hebrew. Both v and b sounds are represented by the same letter, the letter ב, but the sound b is represented by the letter with a dot inside (known as dagesh) and then it's called bet, while the sound v is represented by the letter without the dagesh and called vet (Wiki article for the letter). Here is how they look: בּ vs ב.
In Arabic, Abraham is called Ibrahim, also with b, but the Arabic language has no v sound so it's understandable that it's replaced.
What is the source for the change is the sound?