I've had problems like this twice in my recent game. While I handled it a little differently each time, at the core was simply saying "no."
The first case was just that. "No." Someone was coming into a game we'd already started, and wanted to play a cleric. I told him the people of the world we'd created were ancestor worshippers, but otherwise it would work exactly like the playbook. It's just that his cleric would be appealing to a venerated ancient rather than an all powerful god. So I asked him who this paragon of his people's history was. He answered he was the patron saint of healing, named Meow.
I shook my head and said no, I wasn't introducing that level of silliness into what had been up to that time a pretty serious game. Choose another name.
The other player had introduced a character based on the lead singer of a heavy metal band he'd been listening to on the drive over. Everything was based on if it was "truly metal." With him, I said that he could use this as a source of inspiration, but I needed him to work with me to make this more than a punchline. He still needed to fit in the world and the party, and he nodded immediately and said he both understood and was willing to work with me. In the end, he was without a doubt pushing the boundary of silly with each game, but he did keep it just on the edge instead of blasting past it.
I love the player contribution to world building present in DW, but I don't think it gives players a free pass to do whatever they want. There should be some general agreement of tone everyone works within.