Well he has always had stuff like the best page in the universe and so on. He COULD likely successfully argue that it is a part of his branding that is distinct from what Dick does. Apart from the Biggest problem in the universe, Dick has not followed that pattern of naming.

It is on the other hand a integral part of all naming schemes that Maddox has. I used to be a professional painter, and even when collaborating people get to keep their personal copyrights like character for example. For example when there is a Marvel vs DC crossover comic that involves some Bizarro-Batman that does not exist in other DC comics does not mean that Marvel has the right to use the Bizarro-Batman. But DC can later use the Bizarro-Batman because they have a previous history with the same character and de facto anything that is characteristic like that automatically decides who the copyright belongs to. This COULD be more cleanly done with a written contract, but without a written contract explicitly mentioning the ownership of the copyrights it might be hard to argue copyright ownership over some intellectual property that is so characteristic.