Depends on how I'm playing. My most recent play through, I played a Tribal who had left his tribe to explore the outside world a bit. He took a job as a Courier to make some caps, and after the job (which was to be his last,) he would return to his tribe after spending the caps on the needed supplies for him to make the trip. But of course he gets shot on his last job, and when he wakes up, he can't remember what tribe he's exactly apart of.
Basically he just ran around that entire game, in Great Khans gear, thinking he was a Great Khan until he left for Zion and started getting flashbacks to his actual tribe.
I really dig the Great Khan armor as well, and I would like to do a true play through as one of them, using lever action rifles and sleeping outside, no housing. But it svcks that their armor is factioned based and I never get Legion or NCR assassians to come after me when I wear it. And I really enjoy having a random shoot em up gun fight every couple days with those assassians.
Maybe you have had better luck running into them while wearing the khan armor? If I do a legion playthrough next, maybe i'll try their armor again.