This is great advice, coming from experience. The only thing I would add to it or modify, is that I believe you can claim a trademark without having registered it; but only if you actually did business under that name. If I open up Sally's Pizzeria in town and build my pizza business up for ten years but never register the name, then some joker goes and opens up another Sally's Pizza on the other side of town, I'm pretty sure I can sue for trademark infringement even though I didn't register it formally. Whereas, if I registered "Sally's Pizza" as a trademark but never actually opened the pizzeria, and after ten years try to sue the guy running an actual Sally's Pizza, I'm probably not going to win that claim.
I think the OP's former bandmate has gotten confused between trademark and copyright concepts. They're both types of intellectual property, they both can be created presumptively by simply doing something (running a business, writing a piece), and they can both be registered in order to document one's ownership of them. But the difference is in that second quality, the presumptive creation of the right; If you write a song, you own copyright in the song. But to own a trademark, you need to actually do business under it. He's thinking of the name of the band as though it were a song he can own as a copyright matter, without the doing-business part. That doesn't fly. For instance, Peter Banks was the one who came up with Yes' name as a band (he was the original guitarist); after a couple of albums they fired him. He didn't take the name with him; it belonged to the band.
But I think you do have a point that any creative work he DID do, like an artwork or logo, he may have a copyright in. Even there, I'm not as worried, though. If he did them when he was a member of the band, say with the band functioning as a partnership, and if there was an understanding (as I think there would have been) that these works were done for the partnership of which he was, at the time, a member, then he may not have a claim to separate individual ownership of them; it could be pretty strongly argued that the partnership as a whole owns them. He didn't produce them as an independent outside contractor for them, but as a member of the group.
Of course, we're parsing legalities in an issue which, to judge by the OP, is probably not much more than a garage band with nothing at stake. I seriously doubt anyone's going to court over any of this.
