You never need an account to play. If you have one (it's made when you sign in with Game Center, Play Games, a Unity account or a code, to keep your trophy case and settings on every device), you can delete it, and everything kept with it, for good.
In the game
Settings › Account › Delete what's kept online. Your account with us and the trophy case and settings kept with it go straight away. The trophy case and settings on the device you're using stay, and nothing's kept online again until you turn Keep it online back on.
Game Center's and Play Games' own achievements are Apple's and Google's, and stay with them.
Without the game
Email support@bladesandbiscuits.hockey from the device's account you'd like us to find it by, or tell us which platform you signed in with. We'll delete it and reply when it's done, within 30 days.
Your Unity account
If you signed in with a Unity account, the account itself is Unity's: delete it at player-account.unity.com/delete-account. Deleting it doesn't delete what's kept with your Blades & Biscuits account: do that above first.