Well, this is relatively easy to handle. Let each parent do their own thing, and stop overthinking it. In fact, "stop overthinking it" is really good advice to all new parents. In 15 years, you'll look back at everything you were really concerned about, and realize you hardly care about any of it.

The comments, predictably, have many people asserting that if you let your kids call you by the first name that means that they don't really respect you, or that you're more interested in being the friend than the parent, and all sorts of similar bits of garbage. None of this is true, of course. Literally none of it.