But, do go for quantity. This is not a new problem. Out came 250,000 combinations, and 600 names were examined as possibilities. But only 24, a mere four percent, had no conflict with existing trademarks. Don't shortchange the equity in your name.
Names can carry tons of stored-up value.
Wells Fargo Bank once merged with a larger bank named American Trust Bank Company. Do look within. Sometimes good naming is more common sense than courage. Don't take every name literally. Your customers don't.