They couldn't win anyway.
1. You can't copyright a name, they'd have had to trademark it (unless that is the case)
2. Copyright laws are not internationally viable
3. The usage of the name Batman in no way harms the village of Batman, and is used in an entirely different context
There are six Birminghams in America. The largest Birmingham is one of the major British cities, in the West Midlands. So here - even in the same context (which the Batman case is not) no suing can happen.