There are limits in many places, sometimes in response to that time the artist Prince changed his name to a symbol, in some cases all special characters are banned too, so good luck to anyone with a non-English name. But outside of that? In most states you could probably name your kid Dwayne Elizondo Mountain Dew Herbert Camacho, much worse names have happened.

I think there's been a couple of times where states have tried to stop individuals who have tried to name their kid Adolph Hitler or just some racist slogan, but I don't remember how those went, it was a genuine legal question if those names could be blocked.

Name changes, however, are a different thing - often requiring a judge to approve them, they can be rejected simply due to the misfortune of being a trans person in Texas, for example. Unless it's a name change due to marriage, those are significantly easier for some reason.