Lean Domain Search is a website that generates dozens of domain name candidates that combine your keyword with hundreds of others. The results displayed are only for available domain name registration. Because of the quantity and the quality of the suggestions, this is the best system I’ve ever used, and miles ahead of the “suggestions” GoDaddy and NameCheap provide.
You can access this free tool here: http://www.leandomainsearch.com/
And though it was invented to find domain names, it can be used effectively to generate business and product names just as easily.
Also, if you have a business name and someone else has the domain name, plug in your business name to find appropriate domain names the system generates by adding words that go with your business name.
Give it a try.