This article describes how to rename files that are stored in the G Drive. Please see also the article About Folder And File Names.
Navigate to the file that you want to rename in your browser. See G Drive Browser Navigation to learn how. Right click on the file that you want to rename, and you will see a pop-up menu that has Rename action:
Click on the Rename, and fill in the new name. See the article About File Names for some hints on choosing useful file names.
In your G Drive App, navigate to the file that you want to rename. Touch the three vertical dots to the right of the name to see the popup menu. Swipe the menu up to reveal more options, and then touch Rename.
While editing the document, enter the new file name at the left top of the window:
Note that unlike programs that run on your computer, you do not need to take any action - there is no "Save" when using cloud apps. The content is always immediately updated in the cloud - provided you are connected to the internet, of course.