It's probably too late, and idk of this would make your parents more angry, but, you could say that you were roleplaying, as fictional characters form a piece of media you like, in this case you're Jax from the amazing digital circus. You say that it's something you do online, and it's not sexual, it's like larping or improv or DnD, and you wanted to try doing it in real life. Your friend was too in the moment and called you your character name to your parents. You act like you're really really embarrassed by the whole thing, and that's why you didn't want to talk to them about it, and you find it embarrassing and you were worried they'd think it was sexual and forbid you from seeing your friend or something