In reply to Font name menu order in Adobe apps:
The specs for "Menu Name" (NameID 18):
Compatible Full (Macintosh only); On the Macintosh, the menu name is constructed using the FOND resource. This usually matches the Full Name. If you want the name of the font to appear differently than the Full Name, you can insert the Compatible Full Name in ID 18.
There is nothing in there related to this name mangling.
I didn't test what happens when you use a different Menu Name ('cause I'm on Windows right now), but it's a reasonable assumption that even if you insert a 'different' name here – and InDesign actually uses this –, the result still goes through the "smart sorting" routine.