Do you want me to call Jon Stewart?
Sure, I like his comedy

(although I think in the earlier parts of the Bush presidency it was better - more material I guess).
But seriously why
would a name change be necessary? Especially if it actually became democratic? Such a situation would be more like East Germany finally living up to it's official name and if reunification doesn't happen it would probably require that West and East Germans actually be rather cool at the prospect of reunification, hence it might require East Germans actually being attached to their country and it's separate existence and identity (just not it's communist system).
It would be sorta like having Cuba
needing to change it's name just to reflect a change in it's political system if that ever happened. Cuba was the Republic of Cuba before going communist and has been the Republic of Cuba since going communist and would probably remain as the Republic of Cuba after communism (if that happens). The reason for this is a strong identity with "Cuba" and it's name which is divorced from how Cuba is run. If under any scenario East Germans don't have a strong identity with "East Germany/the German Democratic Republic" then it seems unlikely that reunification would be prevented in the first place so as to bring about the question you raised in the OP. In the other eastern European countries there names were changed when they went communist to reflect their new communist systems so of course a change was seen as being necessary, but with East Germany there isn't anything to change it back to, since the whole identity of East Germany was created in the 1950s as "the German Democratic Republic".
At most they could probably attempt to adopt the former identity of the Weimar Republic (that would have the problem of adopting/referring to the identity of a united Germany...), but I can't see the Four occupying powers being happy with a German state (with a capital in Berlin no less!) readopting the name "Deutsches Reich" .
