The only service that cares about the contents of rDNS is mail. While RFCs don't care what the rDNS says, many server administrators assign penalties to servers where the rDNS doesn't match the name of the sending mail server. Unless you've changed the default exim.conf configuration, DirectAdmin's exim configuration sends email as the hostname. That's why you should use the hostname.
(And incidentally, that's also why you shouldn't use different names to send email; why you should always use the hostname, since you can only have one rDNS record.)
(Yes, you can put in more than one rDNS record if you host your own rDNS, but it's against the RFCs, and the result is unspecified; your system may return more than one, but the resolver doing the query could either return more than one (in which case the program asking the resolver may crash, or accept the first one, or accept one at random), or the first one, or none at all. Since it's not defined in any RFC, there's no telling what a program will eventually get.)
You should be able to change your hostname just through the DirectAdmin interface. It may leave some unused files on the server, but they shouldn't cause problems. I have no idea what it might interrupt or with what it may interfere, because I have no idea what you've made dependent on the hostname. (For example, some of us send hostname information in our welcome emails.)
Jeff