Recover iTunes username (email)
If you sync with an iTunes library, hopefully you have authorised it with the account you used to purchase the app. If so, then the app would be in the “Apps” sidebar item. Click on it and press command+I. The General tab will tell you about which account purchased the item.

If you don’t sync with an iTunes library, your only option is to go to the App Store, sign in with all the accounts you know one by one, and check the purchased items for that account.