How do I rename an Automator Service?

While working on automator services, I sometimes want to rename an existing service for a variety of reasons -- typos, changed my mind, changed the nature of the service, names are too similar, it got saved as "Untitled 2.workflow", etc.

A thread from 2010 suggests simply using the "Save As" menu option. How to rename Automator actions in Services contextual menu? That, unfortunately, leaves the old service hanging around in the list under System Preferences > Keyboard > Shortcuts > Services. And I have run into the problem described in that thread, that if I use Finder to rename it, the old name continues to appear in the Services menu of apps.

In my 10.12.6 Sierra system, there is no "Save As" menu option in Automator. There is a "Duplicate" option, which does the same thing, including leaving the old version around.

So now I have Services named Untitled 1 and Untitled 2 that I need to get rid of. And I know this will occur in the future so what I really want know, in terms of learning how to fish, is how do I rename an existing Service?

If the best method is creating a new one and deleting the old, so be it, but that seems a very 1960s way to do it.

Are there smoother ways to do this?

Thanks.