This is a problem that is straight up forced down people's throats when they take shahadah. Like the next day after I became muslim, someone presented me with a list of "muslim names" I should change my name to.
I didn't change my name at all; I had no desire to become Umar, or Ala-ud-Deen, or Bilal. Frankly, I think it is presumptuous for converts to change their names (unless their name has a pagan meaning, of course) and tends to cause major problems with their families.