technically its actually kind of important, to specify origin nation, as it can affect a lot of things, either directly or indirectly, such as: a few base skill, trait, and attribute mods, equipment availability (not issued by the unit but "starting gear" initial combat units (vehicle, mech, fighter etc if not provided by merc unit)
note I am not saying these are hard and fast rules but guidelines.
for instance it is not unheard of for a steiner or davion MechWarrior to have a panther or dragon mech but it is strange, and the mech is a lot more likely to have issues due to limited availability of "proper parts" this is definitely possible to rectify while the unit is working for kurita (if they allow you access to the suppliers) of course it works the other way as well