After saving a nested search as a smart overview, the name is usually shortened or changed. To recognize what I searched for afterwards, I orient myself by looking at the displayed tooltip.
In the displayed tooltip, I see an overview of the search criteria.
There are 2 ways I know to change the name of the smart overview:
While the search window is still open and the suggested name has not yet been saved.
The cause is that the name field in the save sheet does not only set the title of the overview, it also gets stored on the saved filter itself. The tooltip is built from that filter, and a filter that has been given a name reports the name rather than describing what it actually matches. That is why the long way round works: renaming in the sidebar only changes the title and leaves the filter alone.
It also explains why it looks fine if you accept the suggested name, since in that case the name and the description happen to be the same text.
I will get it fixed so the tooltip always describes the criteria, whichever way you named it. In the meantime the sidebar rename is the way to go, as you found.
Thanks for working it out so precisely, the two screenshots made it very easy to pin down.