Any recommendations for coming up with a good business name?
Most of it is answering the question "Who the heck are you and why would we want to use you?"
What kind of customers are you looking for? Big, boring commercial-real-estate law firms or edgy graphics-design startups? Businesses, gamers, or fanboys?
What are you offering? Huge, multi-million-$$ transaction processing, family reunion-scheduling utilities, or contracts with county high schools for their student websites?
Who are you competing with? eBay, Craigslist, YouTube, Monster.com, or AskJolene.com?
What do you do cheaper, faster, or with fewer errors? Pick two...
How much do you plan to expand? "Joe's Websites" is not necessarily a good brand name if you're planning to become a huge company or someday sell it to people who aren't named Joe.
Since you're running websites, another question might be why you're trying to come up with "a" business name. You could create a dozen web-design businesses (and domains) designed to appeal to all of the above while having a back-office operation incorporate them under a generic umbrella name like "Command Performance, Inc." for legal/tax purposes.
So maybe it really doesn't matter what name you start with, or how many attempts you make. You could run as many as you want for a year or two and then decide what you want to keep.