Hello, my son and I were lucky enough to get the Unicorn. He's a little excited. For the rainbow markers effect of not allowing a character to attack Deadpool, will that protect any character named Deadpool?

No i cant quote the exact rule but when a fig says its name it applys to that fig only

When a power lists the characters own name, it is referring strictly to itself, that one instance, even if you have more than one of that same piece. The power would need to say 'characters named...' to affect others with the same name.

[C]When a game effect allows a character to create and/or place tokens/markers, those tokens/markers, abilities/powers that character can use that affect/interact with those tokens/markers, and the effects of those tokens/markers only apply to the specific character that created those tokens/markers and not all same named characters, or characters that can also use that same effect that creates and/or places those same tokens/markers .

The bolded part clarifies why it only applies to Unicorn Pool.

Hope this helps!