The way that I have found to change the order in which contacts are saved is this: open the view backup storage from the main screen on the app. Open Backup folder. Open Contacts backup folder.

Now in here at the top left of the screen, there are three dots with three lines next to them (it is a button) and press that. You should now be able to change between time, name and type. 

Edit contacts on iPhone

In the Contacts app , assign a photo to a contact, add a pronunciation and pronouns, change a label, add a birthday, and more.

1. Tap a contact, then tap Edit.

2. Enter or update their contact information.

3. When you’re finished, tap Done.

To change how your contacts are sorted and displayed, go to Settings  > Contacts.

https://cellularnews.com/mobile-accessories/how-to-change-the-sort-order-of-your-ipad-iphone-contacts/#google_vignette

https://support.apple.com/guide/iphone/edit-contacts-iph89a9c71d8/ios