I agree, but I'll add that a minor variant of that "you can call me either X or Y" is really annoying, because in my experience "it doesn't matter to me" is almost never actually true. I see this a lot with students; they think they're doing me a favour by giving me a choice, but they do prefer one of them, and their friends call them one of them, and I end up looking like an asshole for using some other form of their name.

To avoid the appearance of that, it would be nice if instead of "you can just call me X"---which sounds like it's your less-preferred alternative, your second choice, so obviously someone's going to try for the other one---you said "please call me X" or "I prefer if you call me X". Then everybody wins! :)