We recently purchased a hotel and are renaming it. Once I have ownership of the Google Plus page, how do I rename it? Or, do I have start from scratch?
Simply go to the "About" section of your page, then click on the name in the header. (You should get a tooltip that says "Edit your name".) You may need to choose to "Manage" your page.
Then simply edit the name.
See also: Getting started with Google+ pages