How can I rename a Sheet in Altium Designer?

As mentioned, you can Save As, which saves a copy of your document. However, the correct way to do it is to open the Storage Manager panel (System-->Storage Manager):

From within the Storage Manager panel you can right-click on a file and choose "Rename".

I would show a picture of the storage manager but mine contains confidential files from my work, but I'm sure you'll be able to figure it out.

Hope this helps!

Right-click on the file in the Project panel and Save As. But then you will have to delete the file with the old name, anyway.