I ask the following in all seriousness, what is your idea of a "fully qualified name" for a Query Layer? Is the fully qualified name the first table referenced in the SQL that defines the Query Layer? Or, is the fully qualified name the name of the layer file on disk when/if the Query Layer is exported as a layer file?
I think this boils down to a difference between expectations and implementation, i.e., Esri's implementation of Arcpy Describe's baseName for feature layers and table views doesn't line up with what you would like to see. That said, I don't think Esri's implementation is necessarily wrong, just poorly documented.
Looking at the Describe—ArcPy Functions | ArcGIS Desktop documentation, baseName is a Describe object property, i.e., it is a generic property and not a property specific to feature layers or table views.
Summary
The Describe function returns the following properties for all Describe objects.
Properties
Property | Explanation | Data Type |
baseName (Read Only) | The file base name | String |
So, what does "file base name" mean in the context of something like feature layers or table views that don't exist as a file?
For several Describe object properties (baseName, catalogPath, path) of feature layers and table views, Esri maps the properties to the properties of the underlying data source. I personally disagree with this decision; but regardless of my personal view, Esri doesn't document this decision and it leads to confusion.
Query layers represent a unique kind of feature layer because the data source isn't a specific feature class or table, but an SQL statement. When a feature layer references a feature class, the mapping of baseName to the underlying baseName of the data source is straightforward; however, that mapping gets much more complicated when an SQL statement can reference any number of feature classes or tables.
If you have specific suggestions/ideas on how baseName should be populated with query layers, the path forward at this point is to submit an ArcGIS Ideas and a formal Enhancement Request through Esri Support.