Good morning, Sam.
Well, it may not be quite that straight forward. Part will depend on the version of Oracle you're using, which type(s) of SQL authentication, which platform you're on, which modules you may have implemented (Apps, RAC, etc.) and lastly, your backup solution. (I'm probably missing some, but this is all I can think of at the moment. I'm sure others will chime in though.) :-)
The GOOD news is, for a vanilla install of Oracle using TNS, it's fairly straight forward:
-- Server side tnsnames.ora
-- Client side tnsnames.ora
Bounce the listener, and you're good to go.
When you begin looking at some extended features though, you may have a few other things to modify. For instance, if you happen to use IBM's Tivoli TSM in conjunction with RMAN on an AIX platform, you're going to need to change your /etc/hosts file, tdpo.opt files, and a change will need to be made to the backup hosting server so it knows to point to the new name/IP address.
So, the question could be absolutely simple to answer, or fairly complex, depending on your environment.
I hope this didn't muddy the waters too much.