So what you’re saying is to first kick off a new run and then rename the underlying Pipeline Task, which will cause that particular run to become a new pipeline name?

Correct, basically you are not changing the "pipeline" per-se but the execution name of the pipeline, if that makes sense

What would be most ideal would be to be able to right-click on a pipeline run and have a “clone” option, like you can with a task, where you can start a new run with a new name in a single step.

I tend to agree, I think naming the pipeline execution run, in the UI makes a lot of sense to me.Any chance you could open a github Issue with this request ?