I don't know of a way to tell if a specific copy of Office has been
registered. It doesn't really matter since registration is optional.
Since the EULA allows one transfer of the software, yes, it is possible to
change it over to someone else's name. That person can access the
registration page if she/he wishes by going to "Online Registration" under
the Entourage, Excel, Word, or PowerPoint menu.
To personalize the copy of Office X for the new owner, if he/she is using
the same computer, that person must delete two files so he or she can enter
his/her own registration information. These files are:
Microsoft Office X/Office/OfficePID
and
~/Library/Preferences/Microsoft/Microsoft Office Settings (10)
The first file is invisible; you can find it using File -> Find:
Name Contains OfficePID
Visibility is Off