I don't know the answer to your question about Project names and importing from Aperture.
But you had better think about changing your initial workflow. LR doesn't really do Projects. You do that by placing images in folders with a project name at the time or before you import the images into the LR catalog. Or use the Collections, which I guess you could refer to collection as Projects, and or Keywords to separate your images into specific groups.
I think you misunderstood me. I'm completely prepared to switch to using "folders" as project names. The problem is, the migration did not carry over any project names, so I lost them all.
For new projects, I will use folder names yes.
Well I never used Aperture and stopped using a Mac for anything well over a year ago so I don't know the answer to your question.
But IIRC from reading other posts about importing the Aperture catalog into LR all that stuff was carried over. That was when using the LR Plugin Adobe provided to do that import. But I don't think that plugin works with the CC/6 version of LR.
Aren't the project names in your Collections panel? They should be.
In general, don't think of Folders panel as equivalent to anything in Aperture. It's about the physical location of your files, not about their categorisation, and the closest Aperture equivalent would be the Reorganise Masters/ Originals dialog box. The Collections panel takes over the role of your Projects structure.