All of the past team up cards have said

or something to the same effect.

However, the team up cards from Batman Team Up do not contain the above. Does this mean these cards can be played regardless of having characters with the same name?

I would assume no. They should really put the rules for Team Up cards in the Comprehensive Rulebook if they’re going to be in every set going forward.

Also, there is at least one card in the set (Harley Quinn) that does have the wording saying you can’t play a Team Up card if you have characters that share a name.