I propose that the user defined folder structure in ArcGIS Online's My Content is replicated in the Catalog window of ArcMap.
I also propose that this structure is replicated in the Overwrite existing service" part of ArcMap too. A search tool might not go amiss either.
Detail of problem
If you share many services on ArcGIS Online, then you will have a very long list in "My Hosted Services" in the Catalog window of ArcMap.
There is currently no way to sort this into folders, even if they are managed as such in ArcGIS Online.
Additionally this problem carries through to the ArcMap > File > Share As > Service > Overwrite an existing service...
The list of items provided there are not even in alphabetical order, so can be hard to browse if you have many services.