I think Big Jude will get a nickname. I'm considering Blue John, probably just called John most of the time.

Big Jude and Little Jude are the same person from different worlds, but they're now in the same world. They not only meet, they live together. (The main setting is something like this.) So they'll be interacting. Their actions are pretty distinct - an embodied adult and a disembodied kid - but even so, referring to them both by the same name would get confusing.

Or is this a story where you're following the same person in parallel timelines or something?
No, but I'm definitely saving that idea for later!