How do I save a Category Report in Quicken

Depends on the report. For the Category Summary report, click the Customize button, top right. Then click the checkbox "Save as custom report" at the bottom of the customization pane.

That said, you should not be using the Category Summary report. It is known to sometimes be inaccurate and is less flexible than the Transaction Report (which can be configured to emulate Category Summary.)

To create a Transaction Report, click menu Reports > Create Transaction Report. When you create a Transaction Report, it is automatically saved unless you delete it. The default name will be shown at the top of the creation window and you can change it there. Once the report is open, you can change the name at the top, or Customize or Delete using the buttons at the top.