This hits on a lot of the same issues we have encountered when trying to name projects or name a business. In order to make name generation less time consuming and automatically handle some of these issues we ended up building a free tool called Mashword (https://mashword.com) to do a lot of the heavy lifting.
Mashword allows a user to enter one or two words and then it will generate combinations(mashups) of the words or alternate spellings, taking into account the pronunciation of the entered word(s). In addition, it will automatically check for domain name availability. If you are looking to name anything, try it out and hopefully it will speed up the naming process for you.