How to delete or change the words "My card" under my own name at the top of "Contacts"? (iOS 13.5.1)
You can’t change those words. They are hard coded into the application and it shows them to identify which contact in the app identifies you.
If you don’t want that contact to be identified as you, go into the preferences for the contacts app and choose a different card under “My Info”. If that doesn’t work, you can delete the card and re-add it, but without choosing the card as your contact details.