How do I rename compound clips?

Actually, I think if you open the compound clip in the timeline, you can adjust the contents so that you can add handles.

It's a bit unwieldy, but what you can do is insert slugs at the beginning/end, change their duration to whatever you want to add to the compound clip, and use the position tool (P) to drag the original clip in the compound clip backwards (or forwards), which will let you overwrite the slug with content.

You might have to readjust the in/out points of the compound clip in the storyline it is used in.

I think the only way to do this is under the Info tab in the Inspector.

But once you've made compound clips they lack handles, and if you ever need those handles back you have to break the clip apart - and lose the name you've applied.