There are unregistered trademarks as well as registered ones. Usually the "TM" symbol is applied to unregistered trademarks, and the ® symbol for registered ones. Both enjoy protection, although it's generally an easier time in court when your trademark is registered.
Whether actively defending your trademark is actually required is a bit of a nuanced topic. Generally, trademarks can be lost through genericide (the mark becomes a generic term for the type of product) or abandonment. Abandonment happens when either the mark owner stops using the mark itself, or takes an action that weakens the mark. The question, then, is whether failing to defend infringing use constitutes a weakening action. Courts differ on this, and there is a large gray area between "we didn't immediately sue a local mom-and-pop shop" and "we allowed a rival company to use the mark erroneously across several states for years without taking action."
In this case, the name is already so generic that you might even be denied a trademark in the first place.