I believe the name that appears for a collaborator is driven by their Airtable account. Only by changing the account details will the display name change, though it will likely change all references to that name, not just new ones going forward.
In the main Airtable workspace view, click the icon in the upper-right that’s the user’s profile image, then click “Account.” In the page that opens up, click “Edit name” next to the current name to edit the first and last name for that account.
I can’t test this theory as I don’t have any collaborators working on my bases (and I don’t want to mess with my own account), but that’s my gut feeling.