First - IANAL - Want legal advice call a lawyer.
Do you own a trademark on the name eyeRoller? My guess is no.
There are two kinds of trademarks. One is a registered trademark. That is shown with an (R). And this means that you filed it with the uspto and obtained a registered mark. Then there is unregistered trademark which is shown with a TM. This is also known as a common-law trademark and is also valid in the united states and canada and some other countries. For that you just stick TM on something and use that mark in print or advertising.. like on a website or inside a published app.
If you do own a trademark and you believe the other party does not - you can contact apple legal ([email protected]) and they will ask the other party to either prove that they own the rights to use that name or take down the app in the USA store. I have followed this method and have gotten other apps taken down. But if it gets ugly you might both have to take the app down until going through an expensive legal battle.
But looking at your case, I doubt that you own the trademark over them since their game was released in 2010. Actually it's more likely that you are infringing on their trademark. And in that case it might be you that gets the takedown letter. Has your game been advertised since 2010? Sounds like you just published it the other day.
So here's what you can do:
Change the name of your app to something that doesn't infringe on someone else's trademark.
Or leave it up and don't worry about it. Wait and see what happens. Tons of apps have similar names. Probably no one will do anything. But if they do you'll have to take yours down.
In the iOS app store there are easy tricks to get around taken names. The name of your app in the app store can be something like "eyeRoller game" and the app icon can still say "eyeRoller". So you can still publish on the app store.
* EDIT *
I reread your question and realized that you know that you might have to change your name. So hope I didn't come off too harsh.
The easiest thing to do is to change your name very slightly. "eyeRoller Prime" or extreme or whatever. Having more words in your app name adds to your SEO. It's like getting extra keywords. So it won't hurt sales to have a longer more descriptive app name. And the visible name can still be the shorter version if you want.
I did a photo editing app called "Silver" - but there were lots of other apps called Silver so I called it "Silver photo effects and editing". This isn't a plug cause the app is no longer available. But the point is that the more descriptive name isn't a bad thing. And you can wait to worry about a takedown notice until you get one.