what other titles would the second and third film get then?

we know FFC wanted III to be called: The Death Of Michael Corleone.

What would the name of II be?

Personally, I think that without the "PART IV" mark, the movie would distance itself from the trilogy. This could mean that it might even work but on the other hand, then it wouldn't be a part of the movie franchise anymore, to my opinion.

The Godfather Part II: A Rise Of Father And Son or something