How To Change Your Facebook Account Name From Your Android Device

Facebook allows you to change your name. You can easily do it from the web interface by going to the General setting page.

You can also change your Facebook name from your Android device using the Facebook app for android or any of your device's browsers.

Facebook App For Android;
If you have the Facebook app installed on your Android device, launch it.  Then tap on the Facebook menu button in the upper right side and select 'Account settings'.
 On the account settings page,  tap on the 'General' tab and select 'Name'.  You can now edit the name as you wish.  
Tap on 'Review change'  and save the changes if Facebook accepts your new name.  You will need to enter your password again before the change is effected.

Facebook forgot password

Your Android Device Browser:
Whether you are using the default Android browser,  Chrome for Android,  Firefox for Android or any other browser,  you can access your Facebook account and change your name.
Login to mobile.facebook.com on the browser of your choice.
Tap on the Facebook menu  in the upper right side.  Select 'account settings'.  On the account settings page, tap on 'General'  and proceed to change your name following the instructions above.

Here are some rules and guidelines from Facebook about Facebook names and changing them.