Na, names are about pronunciation (how you call someone). Written letters are an approximation of that. You can't pronounce a newline, so there's that.
But that doesn't really address the original question, does it? You don't have to pronounce all the letters in a name, so the fact that you can't pronounce a newline isn't sufficient to demonstrate that it can't be part of a name.
But something has to be written on the birth certificate and social security card, and that's what everything else will expect you to use. I think just due to technical limitations (e.g. of the printer/template for those things) it wouldn't be allowed, but I dunno about legally