Why Abraham and not Avraham?

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?

Neither Latin nor Greek (at the time of Biblical) translation had the orthographic means (or need) to represent the contrast be /v/ and /b/. These were the source of the English versions of these names (not the Hebrew). They have been further distorted by letters assigned their English, rather than Latin, values. The result is that many names Hebrew names are pronounced in ways that are unnecessarily far from the original, given the sounds at English speakers’ disposal. Besides the /v/-/b/ neutralization of Abraham, Absalom, Reuben, Job (all with /v/ in Hebrew), there are:

• all the J-names (Job, Jonah, Jehovah) which have /y/ in Hebrew;

• those containing v (Eve, David) which was /w/ in the Hebrew;

• those containing /ð/ (as in English the), for which d substitutes (e.g., Gideon, Gad, the second d of David); and

• at least some instances of s for sh (e.g., Absalom, Menasse; but, for some reason, in Shem, sh survives fine).

The survival of /θ/ (e.g., Jonathan) might be attributable to Greek, along with ch for Hebrew /x/ (e.g., Enoch).