Well or Wells would work, but the natural one is Max and that's what people are going to tend to call him. My cousin has a Maximillian (they're in Germany) and they call him Maxie which I think is cute.
Max without a doubt. And I don't think that is just because I live in a rainy climate that I think giving a kid the same NN as a pair of galoshes is a bad idea.
Re: Nicknames for Maxwell?