On the computer

Debian

Reference: Debian WIKI page on changing hostname.

Slackware

As root either run netconfig (full prompted re-configuration requiring IP addresses and domain name) or do it the manual way by editing:

1. /etc/hosts
2. /etc/HOSTNAME
3. /etc/NetworkManager/NetworkManager.conf (if it exists)
4. /etc/rc.d/inet1.conf (if supplying hostname to DHCP server)

then run /bin/hostname $(cat /etc/HOSTNAME | cut -f1 -d .)

If running or using any of avahi, CUPS, ejabberd, Exim, /etc/motd, OpenSSH server, ssmtp or sysklogd then read the  Debian WIKI page on changing hostname

Ubuntu

Not tested: as root, edit the new host name into /etc/hostname and run  start hostname

Not tested (may all be done by the command above): if running or using any of avahi, CUPS, ejabberd, Exim, /etc/motd, OpenSSH server, ssmtp or sysklogd then read the  Debian WIKI page on changing hostname.

On other computers

DNS servers

On DNS servers which have record(s) for the old name, change both the forward and reverse data files.

In Blue Light, at least rose runs this sort of DNS service (backupserver's DNS service is caching only).

/etc/hosts files

On computers with an /etc/hosts file which has record(s) for the old name, change the line.