Sam, it took my husband and I pretty much three solid years to come up with our business name so I'm about the last person to give you advice on that!
What did finally work though was I made a pact with another new breeder (we'll both ship out our first hatchlings this year) that gave us about 2 weeks or so to each come up with names. We had a solid date to do so. Then we just talked on the phone and on the computer. Just free flowing thoughts about our businesses, our names, our locations, our dreams, etc. and bingo! we both now have names we love, websites to build, etc.
The thing is though, Sam, if you are a few years away from selling or trading anything you'll be spending money to register a name and hold a site with nothing to put on it. For me, until we were really close to being actual breeders (even in our small way) it just wasn't worth the cash over the years.