1/4-20 Cage nut? - search for that name.
Mine look like they were pressed in and don't jiggle around like the arm rest cage nuts. I looked from behind also.
An option would be a cage nut or a nutsert. Either one would modify the hole in the door panel slightly.
https://www.mcmaster.com/cage-nuts (see Steel Snap-In Nuts at the end of the page).
This guy had a similar problem -
http://67-72chevytrucks.com/vboard/s...02&postcount=3
Nutserts:

There are also the hand drawn units:
https://www.pegasusautoracing.com/pr...sp?Product=655
Harbor freight sells a cheap set up -
https://www.harborfreight.com/45-pie...-kit-1210.html