First log on your Facebook and then SETTINGS , a windows opens as your MY ACCOUNT and display options are as Settings, Networks etc.
Select SETTINGS and then a window open as MY ACCOUNT and under this there is first option is NAME and click on CHANGE and then a new window open and there you can enter first name, middle name, and last name,, Full Name or Display name.
Select SETTINGS and then a window open as MY ACCOUNT and under this there is first option is NAME and click on CHANGE and then a new window open and there you can enter first name, middle name, and last name,, Full Name or Display name.