[Inziladun]

This public computer for some reason will not allow me to quote, but I'm with Zigûr that the Mouth was not necessarily old, just that he had so submerged himself into Sauron's will that he had lost any sense of independant identity. It need not be assumed that Gothmog was in any similar state. He was probably just an Easterling, or maybe even an especially large, strong, and commanding Orc given that particular name in honor of Morgoth's fearsome field captain.

I also agree that the Nazgûl would have been unlikely to have kept any connection with the peoples of their origin. There would have been little need for it, given that Sauron already had a hold on those folk anyway.