where does `hostname -f` derive the domainname from?

[Jim Popovitch <jim@k4vqc.com>]

where does `hostname -f` derive the domainname from?

I have 2 systems, the first was buster --> bullseye with /etc/hostname
containing "oscar" and `hostname -f` returning "oscar.domain.tld".

The second system is a clean install of bullseye with /etc/hostname
containing "felix".  On this system `hostname -f` returns "felix".

DNS for both systems have FQDN entries.  Where should the domainname be
set in a clean fresh install of bullseye?

tia,

-Jim P.