you can't really have a 'nonsense' name - there's a list of around 3000 characters you're allowed to use in names, but in theory, you can put together whatever you want. you'll just get side-eyed for having a weird name, that's all.

that being said, i think most of these websites that ask for a kanji name will require you to show ID with that name when you show up in person, so you might run into trouble if you just pick random characters.