I started a service, once upon a time, and to keep a clear separation I figured I'd register a company, get a company bank account, etc.

In my case the actual product was a website, and that had a name which was good. The actual company itself was less important - the only time folk would see it would be on cheques, or invoices.

on that basis I figured I'd take the first name that sprang to mind, and I became "Pink Pony Productions"; a name shamelessly stolen from a throwaway line from Lisa Simpson - Episode "The Ziff Who Came to Dinner".

So: Product name / Website name / Service name == Important, but company name / startup name .. less so.