The thing you should remember is that Hebrew and other Semitic languages don't bother to write down the entire word, unless it's vitally important (like the name of god). They just write the consonants. In the case of Rebecca, this would comfortably give you R-B-K, and you could fill in the vowels yourself.
In English we don't find the -bk- combination comfortable, so English people felt that sticking another -e- in to separate them was an improvement. So Rivka becomes Rebekah, or Rebecca. (Same thing happened with Yahweh and Jehovah; the Y -> J is also pretty usual, and Jehovah has a more English sound!)
As for the -V- turning into a -B-, this is pretty normal. In Hebrew they spell Deborah with a V - Devora - and this is just one more example.