I really like Luka & Max together.
ETA - I misread the original query and thought you were looking for general name suggestions rather than middles. Sorry! Let’s try again.
Max Abraham
Max Darius
Max Dominic
Max Edison
Max Ferdinand
Max Leopold
Max Sullivan
Max Tennyson
Max Ulysses
Jude Willoughby
Jude Valentine
Jude Theodore
Jude Solomon
Jude Malachi
Jude Horatio
Jude Gregory
Jude Everett
Jude Callahan