On the website, click the icon in the upper right corner and then click “Account” (theathletic.com/settings). You can change your Name, Email, or Password under “Personal Information”.
On the app, tap the button in the top left corner, and then the button next to “My Feed”. Tap the Pencil icon overlapping your profile image to change your Name or Email, or to link your account to Facebook. You cannot change your password in the app at this time.