How do I change my domain name?
 

I am running a vBulletin website (and love it!). I have two domain names (domainA and domainB) under the same hosting package. My forum is currently using domainA, but I would like to change it to use domainB. Since I am not changing hosts, what are the steps that I must do in order to make the domain switch?

I am a beginner (at least I consider myself to be), so advice is needed! Thank you in advance.