How do you check for an available motorcycle club name?

Just do an internet search of the name you want and see if anything shows up. Be very specific; for example, "Midvale Touring Motorcycle Club". Also, you can search business and organization names via state departments of business sites online. Anything that has been made "official" is usually listed this way. And that is a good way to give your club's name a little protection (you really can't "protect" it from anyone else using it unless you trademark or copyright the name). It rarely costs anything or much to become a non-profit state organization or "business" other than some paperwork and small fee. You will need a "registered" agent (usually founder or president (yes, you can change this in the future)), an address, and you will have to file an "annual report" (usually online and usually just to update information (e.g., officers, address, registered agent)).