Generally speaking, if the symbol, or character, can go into the chat (without becoming a * or something), it can go into the name.
I have a Chinese name (which is close enough to jp kanji, I don't have a good input method for jp), I have gone through about 30 characters, slightly over half of which are blocked, before coming up with a suitable set for my name.

It should be much easier for you to find a set of a few dozen characters you like, dump them all into chat, and see which one can "come out" and then make a selection out of those than keep trying different combination on the name change thing.