Logging into Game Center with Nickname

I have a clash of clans account that I have normally logged into, as I remember with my nickname. This was no more than a month ago; I am not aware of any Apple ID being linked with the game center account. However, I am no longer able to log in with just my game center account, and am locked out of my clash of clans account. I can still access it on the original iPhone, I need to transfer the account to a new phone, and I cannot without the linked game center account.

Can I find the email associated with a game center nickname, or unlink a Game Center account from a Clash of Clans account?

Thank you