I have a module named
If you are using Sugar 7.2 , then it is simple,
1. Go to
Admin->Studio->Modulename->fields->Select custom field.
check Calculated Value then click on
Edit Formula .
3. From Fields select your name field.
4. Then Deploy it.
Now go to your module and save your name it will appear on your custom field also.
I did not work on Community Edition But i can give you an idea that , you have to write a
logic hook after save , in that hook you can write logic to copy Name to your custom field.