No, it won't be neccessary. However, your 1931 'alias' (Sonny Crockett/Harry Callahan/whatever) might be forgotten by the characters so you'll be called one of them by default
[I upgraded to a new computer - old one on XP, new one on Win7 - between Ep 1 & 2. Didn't replay Ep 1, so my choice of alias was forgotten. Doesn't really matter though]