There is no exclusive rights forever rule for anything anywhere, but there are issues with trademark law, which does recognize that the first and continuous user of a distinctive mark (whether registered or not) has enforceable rights. Now btc-e is basically a rogue exchange that operates on the gray web and does whatever the hell it wants, so I expect nothing different.

But if another exchange -- say one that is going out of its way to try to be legally-compliant -- wants to pick up Dash, they will probably want to avoid behaving in a similarly rogue manner.