Best way to copy Contact name to Nickname & Legal name
This chapter of the user guide should help you: https://docs.civicrm.org/user/en/latest/organising-your-data/profiles/#updating-multiple-records-at-the-same-time_1

Basically you:


create a profile with the field you want to view + the ones you want to update
Search for the contacts you want to update
With the search result actions you select Batch Update with Profile and use the profile you created