Change the hostname in the files /etc/hostname, /etc/mailname and /etc/hosts. Afterwards run the script /etc/init.d/hostname.sh to set the new hostname on the running system:

root@host:~# /etc/init.d/hostname.sh

Remove the SSH host keys which were generated on the old system:

root@host:~# rm /etc/ssh/ssh_host_*key{,.pub}

and create new SSH host keys for the new system:

root@host:~# ssh-keygen -A

If a static IP address configuration is used, change the IP addresses in /etc/network/interfaces

If postfix is installed change the hostname in the file /etc/postfix/main.cf:

/etc/postfix/main.cf

myhostname = <new hostname>
mydestination = <new hostname>, <new fqdn>, localhost.localdomain, localhost

Update the local aliases file:

root@host:~# newaliases

Reboot the system.