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It's a dark-blue app with a white "f" on it. This will open your Facebook News Feed if you're already logged into Facebook on your phone or tablet. If you aren't logged into Facebook, enter your email address (or phone number) and password to continue. It's in either the bottom-right corner of the screen (iPhone) or the top-right corner of the screen (Android). It's near the bottom of the page. Skip this step on Android. This option will take you to your Account Settings page. It's the top option on this page. You should see this near the top of the screen. Tap the First Name, Middle Name, or Last Name field, type in your preferred name, and repeat for the other fields as necessary. It's a blue button at the bottom of the screen. Facebook will display variations of your name at the top of the screen; tap an option to select it as your name's appearance. You'll enter your password in the text field above the Save Changes button. Doing so will change your Facebook name.
Open Facebook. Tap ☰. Scroll down and tap Settings. Tap Account Settings. Tap General. Tap your name. Edit your name. Tap Review Change. Select a display option. Enter your password, then tap Save Changes.