I've finally managed to figure out what I was doing wrong here. I was using a Windows installer that was using Project Output for the files. Although these files were signed in the bin folder, they were no longer signed after the app was installed.
Instead of using Project Output, I manually added all DLL and EXE files that I wanted included in the installer. After doing this, the company name started showing up when the UAC popup appeared.
I would prefer using project output, since it seems a bit more integrated, but I would much rather have a working solution.