My Band is Releasing it’s First Single. Is Trademarking our Name High Priority?

We are about to release our music this month but we share our band name with many other very small artists. I understand it is unlikely that our music (that will be marketed extensively) will blow up however I don’t want to eventually see some sort of success and see our music taken down because someone else of the same name got the trademark first. It is worth mentioning that the name is currently available under Class 041 and there is a trademark holder for Class 009 for what looks like a completely different industry. Am I misunderstanding how this works or do I absolutely need to trademark the name before doing anything.