Actually, "the dative can be substituted for the genitive" is not exactly correct. It's just that Latin uses a different structure to convey this idea (in this case, what someone's name is).
Spanish and German use the vocabulary equivalent of "I am called..." English says "My name is..." Latin says "The name to me is....." (Kind of like "The name in respect to myself is...")
It's just a different way to express the same idea, but it is not the dative subbing in for the genitive. Latin just uses the dative for this construction.
The dative of possession has a different connotation than genitive.
Using the dative emphasizes the possession itself. At least, that's what I was taught :)
Well, there is definitely a different sense in the idea. The dative of possession, in this case, is not dealing with ownership. You don’t own your name the same way that you might own a horse, for instance.
My comment is primarily for earlier language learners, at which time learning the nuances of the grammar can actually be counterproductive. I don’t go into a dative of possession, and what exactly that terminology means, with my Latin one students because it would overwhelm them.