Step By Step to do it

Go to your Facebook App

Navigate to right at the top click on three lines



Then go to settings & Privacy
Now go to settings

then click on the 
see more account center 



you will see a lot of options
click on the profiles

click on your Facebook name, then rename and click on review the changes


The Facebook Team will Review and changed the the name immediately

Note : You can only charge name in two months which is 60 days, after that you can just review the last name you change, then manage it.

Thanks.