@ ChatPGT,
This is exactly what I have done, over and over again.
Removing T580 from the "Computer name" results in an empty "Computer full name", but when I reenter T580 in "Computer name" the result shows up as T580.T580 in "Computer full name".
I'm not using any domains, but only Workgroup for my LAN.
Btw.: I have searced "Regedit" for the string "T580.T580", but to no avail.