If you have forgotten your iTunes Store account name, you can recover it if you have made iTunes Store purchases by following these instructions:

Note: In most cases, your iTunes Store account name will be your email address. You may want to try signing in using your email address as your iTunes Store account name. 

1. Open iTunes
2. Highlight one of the items you have purchased (You can find your purchases in your Purchases playlist).
3. Choose File > Get Info.
4. Click the Summary tab.

The Account Name area will list the account used to purchase the item. Unless you have changed accounts, this is your iTunes Store account name.