Q: how  can i delete my game center account ? i just lost my phone

Did you have Find My iPhone turned on on the device? If so, and if the thief has the phone online, you can go to iCloud.com or to a Find My iPhone App on another iOS device, sign into your iCloud account, go to Devices in Find My iPhone, click on your device, and Erase it. Erasing it will not remove your Activation Lock, but it will stop tracking the device.

You can, and should, also change your passwords.

Best of luck,

GB

See if you can locate your iPhone so you can disable it >  Apple - iCloud - Find My iPhone, iPad, and Mac.