Rabbi Avigdor Miller said that it used to be that gerim (converts) and baalei teshuvah (repentants) who had been given non-Jewish names did not change their names when they became part of the Jewish nation. However, nowadays, that is no longer the case, and so it is normal presently in most cases for gerim to become Avraham, Ovadyah, etc.
Avram became Avraham, and Sarai became Sarah.
Why did this custom change, and why don't converts Hebraize their existing English name and add a letter of God's name the way that Abraham our Patriarch did?
Also, why do gerim nowadays become Avraham, etc., because if there is nothing inherently wrong with using non-Jewish names back then, so what is wrong with using them now?