+1 for this. The starred items already have an icon beside them that show the user whether it is a saved note or a saved search, and so having names for saved searches isn’t going to be a concern when it comes to confusing either of the two. On the other hand, having no names for the saved searches would confuse the user what each of them does especially if there’s a good number of them, as stated from the previous posts here.
Perhaps having an additional option when right clicking a specific saved search would allow us to add a name or to rename it.