If you can log in:
On the website, click the icon in the upper left corner and then click Account (theathletic.com/settings). You can change your Email or Password under Account.
On the app, tap the button in the bottom right corner that says "Account". Then tap your name at the top of the page. Here you can manage your subscription by: changing your name, changing your email, restoring purchases, manage your subscription, or even delete your account.
If you can't log in:
Change your password at theathletic.com/forgot-password and then move on to the steps detailed above. Resetting your password at the link above will remove your Facebook data as well, so if your workplace blocks Facebook Login to The Athletic, you can reset your password to remove the Facebook data and sign in using Email/Password at work.