The name will have to match. I'm 99% certain you could file to change the name of the LLC and it would be inexpensive and easy. In order to take in revenue you have to have a company in some form -- whether that's a simple sole proprietorship, partnership, LLC or a corporation. So yes, all those little indies do have to have a company behind it if they're selling! If you're going to use that LLC and act in that company's name I recommend filing to change the name to cover your rear.
If it's already, say, Jeremiah, LLC, you could easily go with Jeremiah Games, LLC assuming that name isn't already taken, so that shouldn't be a problem. Google "[state name] business filings" to check your state's website and see if it's available -- you want to look on your state's Secretary of State site for that.
Hope this helps!