I'm a little confused about what you're saying too. Since it's Jewish, as an English surname my guess would be that it stuck as a fixed name after a long line of patronymics. In other words, Jewish last names were typically from the father's name, say
Moses ben
Israel, then his son could be something like
Levi ben
Moses, etc. So in early times the name changed with each generation. My guess is that someone was the son of
Israel and at some point, when last names were standard in English society and passed from generation to generation in the same way, at that point the name stayed that way. Just based on my superficial knowledge.