We would take a nice Jewish name like Moshe Eliezer, and find a really outrageous secular name for it, like Montgomery Ellsworth.
BS”D
I know of a BT whose secular registered name is unfortunately Leroy.
Actually, the Satmar community registers very old fashioned names for male children whose names do not have a clear English translation (Yoel is registered as Joel, Avrohom as Abraham, but Eliyahu could be Eugene or Alfred. The generation before has names like Leopold, Harold etc). This was, for some reason, the way Reb Yoilish ZYA wanted it and it reflected Hungarian custom to use a secular name for government matters.