So if you've seen Ulysses' http://images3.wikia.nocookie.net/__cb20110603140508/fallout/images/thumb/7/78/UlyssesConceptArt.png/818px-UlyssesConceptArt.png, you'd see multiple coat designs. If his coat becomes this way in lieu of who you could convince him to work with, how would it work out for those of us who love Mr. House or the Independant route? NCR and Legion have special faction tags. but I've never seen an option once to support Mr. House or Yes Man in quest/dialogue trees.
Obviously House would be Ulysses keeping the Old World flag, given how House is so focused on recreating Vegas as it was before the bombs fell.
Yesman would be a trollface and would only be accessible on your second playthrough.
Or just a blank coat cuz, y'know, anarchy.