You know it is an angle so the shape is defined as L-angle, there is no double angle unfortunately.
There are:
Two ways of defining a rectangle (Rectangle/Rectangle Bar)
Two ways of defining a round section (Round/Round Bar)
Two ways of defining a hollow round (Round HSS/Pipe Standard). You could wonder what is a 'Pipe Non-Standard'?
but no double anything PFC/Angle...and no ASB.
Then there are the:
I-shape Parallel Flange
I-shape Wide Flange (also parallel flange)
Seemingly the only difference in the above is the connection dimensions. One is for compact section with less bolt space.
I think naming of these things is very problematic. Probably they need to think more generically in terms of separating the section shape from how the section is then used. You could have glulam I-Beam, nearest match would be 'I-Shape Welded' but without the welded i.e. both flanges same width but no web fillet.
Essentially you have I-ParallelFlangeWithWebFillets and I-ParallelFlange. If you then allocate a dimension for each flange width you can make them both the same (if need be) and you get rid of confusion surrounding extra section types for if it is asymmetrical or not. I got rid of the 'shape' in the suggested names above because we know it is a shape.
They should think in terms of this is a common type of section these are the dimensions that define it.
Then separately, the family is a steel section with this class of end connection dimensions associated with it for this section type.
Connection dimensions and section dimensions are interdependent and can be made so but can be defined separately i.e. for this section type I can then separately select from these relevant sets of end connection dimensions for the family.
I may make this an idea, it started out as a simple 'no' answer then became a thought process.