It's never mentioned how Balto got his name in the movie. As for questions, you don't answer them if they've been solved, because they've been answered already. Hence why you cannot answer.

I second the Rose theory, and I think Catwhohas14tails thirds it, because in one of her fanfics she made Rosie protect puppy Balto from being whacked by a man's broom and pretended that it was her dog and named him Balto. No one is quite sure, maybe everyone gave him it, maybe just Rosie did, maybe it's just a joke between the Nome people. Maybe even he or Boris gave him the name so he wouldn't be called a weirdo by other dogs for not having a name, but that wouldn't make full sense, for the humans wouldn't know his name. So, yeah, I really don't have any other ideas for this. Maybe even someone used to like him (such as Rosie, except she still does), named him Balto, got rid of him, and the townsfolk knew him as that. And as for the 'question' question, there's no way to do that unless you REALLY want to and PM the person who asked the question.

I think that's what Rosie might have called him or something, I'm not sure. Nobody knows how the townsfolk know his name.

And you cannot answer a question it it has already been solved.