The actual hostname of your box should be some kind of name, for example let's assume it is anubis. Then the FQDN would be:
and the hostname would be:
Your /etc/hosts should have:
18.104.22.168 anubis.myspecificdomainname.com anubis
where the ip address is available on the outside.
should be an alias to
myspecificdomainname.com which should be handled by your specific nameserver.
As for ssh-ing to the box, the only requirement is that you have the ssh port 22 enabled. Then all you need to do is ssh to ANY name that resolves to your address. you can even ssh directly to the ip address if you want to.