Sometimes to avoid harassment or persecution. ___ This question is best viewed as part of the wider issue of changing family names on settling in a new country. It is not a specifically Jewish...
jewish people had to turn themselves in to get a gold jewish star to put on all their clothes and they went from there(if you didn't turn yourself in they would look at you and assume)
Israelites (Yisraelim in Biblical Hebrew), Hebrews (a term first used probably by Ancient Egyptians) and Bnei Yisrael ("Children of Israel") are all terms used for Jews before the Common Era.