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.