Say you have a game (we'll call it Widgetville) that is web based and will also be extended to mobile devices.
But "widgetville.com" is taken. So your main domain would be something like "playwidgetville.com" or "widgetvillegame.com"
The game itself is, at least initially, completely web based and 100% of the game interaction happens at the website.
The owner of the main domain isn't interested in selling.
So, is it a big enough deal to change the name of the game?
@ship, a few years ago I would have advised that the domain name is very important, I think think so much anymore. There are a lot of web apps springing up with the name app at the end, like tenderapp.com. The fact is good domain names are mostly gone.
The good news is that the owner of the domain name is likely just sitting on it. If you can find a creative domain name that you can brand, then its worth renaming the game. But its a lot more about the game than the domain name.
Plus, with good SEO your popularity for your domain name such as playwigetgame.com or widgetgamerocks.com or whatever you name it will make sure that your product shows up first for results.
The only drawback is that sometimes through word of mouth people might suggest the name of your game rather than its domain, but again with good seo its only a couple clicks away.
Funny, I actually tracked opposite to FrankyB. Nutshell version is that changing the name of the game is much easier, this early in the game, than having to deal with this later.
While FrankyB is right that easy domain names are harder and harder to find, the issue still exists that if your domain name is "playwidgetville.com", many people will type the simpler "widgetville.com" and end up somewhere you don't want them to be. Worse, SEO doesn't solve the issue, because lay people normally pull up Google, enter "widgetville" and if your domain isn't the first, you will bleed traffic. Most people don't type in the URL, they type in the domain name in the search box.
And, to make your link show properly, and keep it first, is can be difficult if you have a popular competitor. (However, if he's a domain name squatter and not actually producing anything, then you may beat him out with simple SEO. Another approach is that you may also beat him legally by trademarking and ACPA. IANAL applies.)
I have had a similar issue with a domain name. I am continuously surprised at how many people end up on a competitor's domain.
With sites like mobile app store it is probably not that important. Most users purchase mobile applications without going to the developer web site.