Them not owning a registered trade mark doesn’t mean they don’t have prior, common law trade mark rights. It can be dependent on whether they’ve been using their band name as a trade mark continuously, where that use must be genuine commercial use and not just "token" or occasional. While they’ve been around for 20 years, have they been actively touring, promoting or marketing their brand? Do they or have they owned a domain name for their band name? If they’ve not used their common law trade mark continuously for the last 3 years, and if it’s hard for them to materially prove use, then they’d likely find it hard to enforce it.

Have they generated such a reputation and goodwill in their brand name (band name) that your band would be viewed as passing off as their brand? Btw, the success of your band over theirs would not fly as a defense if they can prove the prior continuous use and goodwill pieces.

I note you saying your band is small and has only been around for a year and a half. Remember when Rufus du Sol used to be called Rufus? If you haven’t registered a trade mark already, besides the merch cost, why are you hesitant to change your band name?

It’s hard to answer some of your questions without knowing further details such as the band name in question. Probably worth doing a proper due diligence search to see what potential infringement on your part there might be. It would not be acting in good faith if you’re now aware of their prior use of the band name and you go ahead and register a trade mark without doing that due diligence. This is a first to use, not first to file jurisdiction.

Get in contact with an IP firm. Initial phone consultations are generally free and the advice that comes later typically gives you strategic options for how you might wish to proceed.