In the Admin CP, head to Users, User customization, Custom user fields.
Click on Add field. You'll likely use a Single-line text box for this. You can decide whether or not you want to have one field for name or do a separate field for first name and surname.
Under the General options, you can set whether or not the field/s are required. To show the fields during the registration process, make sure you tick the option to Show during registration.
Here is an example I did for 'First Name' if it helps: