Click on the Names button. You will see the following screen:

You can't modify the default/original screen BUT you can clone it. Click on Clone. You will see a small tip screen with a few pointers. You can stop and read it if you wish. Click OK. You will then see the following screen:

This is a copy of the default / original screen. You need to give it a name under Screed ID at the top of the screen.
Put your mouse pointer on the spot where you want a new field to appear.
Right click your mouse. You have three choices.
Select field.
You will then see a list of your fields for Names.
Highlight the field you want to add to the screen and click OK.
You will see a box that says Field Properties. If you want more information about the choices, view the User Defined Fields document at help.htm.
Click OK. Your new field will then appear on the screen.
You can move the field by clicking and dragging it to exactly where you want it.
If you want to set the tab order (the order in which your highlight moves from one field to the next) click on Set tab order. You will see a 0 in each field.
Starting from the first field you want to edit, double click it. It will start numbering them in the order that you double click them.
Once you have finished setting the tab order and you have added all the fields you want, click OK.
You will then see your new screen as a choice on the list of available screens.
Once you highlight that screen name and click OK until you are all the way out of User Preferences, that screen will be the screen that comes up when you go to Names/View a record.
NOTE: If you create many new fields and need more than one screen to hold them all, you can create additional screens to hold them.
Instead of cloning the original screen, start with New.
Add the fields you want and save the page with the same name as the first screen BUT as page 2.
This new screen will appear as an extra tab on your Names screen.
It will be the last tab(s).