Kevin,
An issue similar to yours was raised in the ASTAP forum:
https://sourceforge.net/p/astap-program/discussion/general/thread/40bba8e112/?limit=25#b581
It may be worth raising an issue on the ZWO forum to find out why lat/long aren’t saved when using ASIair (https://bbs.zwoastro.com/)
I think it is possible to manually type in the name of the star when setting up the image capture with ASIair and the FIT files will then have it in the file name.