Yes, of course if she wants to keep Susie, then that would be fine. But if she doesn't want to, then she hasn't got many options. However, Sue is one alternative I guess.
My DD has a formal name, and a cutesy nick name, that some people use as a name in its own right. However, my DD has already said her name is babyish, and when she goes to secondary school she will request to be known by her full name, and not the nickname. Her name, her choice.
Maybe I'm biased because I hate my name, and am known by a nickname (chosen by me and I do like that!) but I personally believe that whilst you bequeath a name, you don't own it, so choosing a name to me is about the responsibility of giving an appropriate gift, rather than just thinking "I'll name the child what Iike". When choosing a name, I personally would choose something with options, so that the child can choose a nickname, use the full name if they consider the name to be a bit babyish / old fashioned ... Whatever the complaint may be!