Supplement to usernames:

ok, to point 2: If I manually assign each individual user in the WordPress user settings that the “public name” (display_name) should be used as the first and last name, then it works.
Do you perhaps know a trick how to set it up automatically? Unfortunately I don’t find anything 🙁

But point 4 in the view of the communication partners would be important if not the name of the last one written, but ONLY that of my counterpart for a better overview.