So, what one or two words would you use to describe the package "Fighter who uses light armor, rides a horse, uses a bow, and exotic weapons" that doesn't carry the baggage that Samurai does?
Take out the "exotic weapons" part and the term is already in the game-- Skirmisher.
But in any event... there's not going to be any Fighter mechanic (whether it be expertise dice or some other thing) that is going to require that specific of a load-out of equipment. We've already talked about this upthread-- if the sub-classes are how Fighter's fight... then we've already seen the terms in the game of how they can be laid out:
Weapon & Shield - Defender
Greatweapon - Slayer
Dual-wield - Tempest
Finesse weapon - Duelist
Loaded ranged - Marksman
Thrown ranged - Hurler
Impovised/unarmed - Brawler
Tactical - Warlord
Other than the Warlord (only listed here because of legacy issues), none of these names imply any sort of world, or specific culture, or job, or scenario/plotline as to why they are that sub-class.
You say 'Gladiator'... that implies who you are, where you learned your technique, and how you got where you are. You say 'Brawler'... that implies much, much less about the specifics as to who your character is... and thus allows you to create your character's history yourself.
If you still question my point on this, then let's turn things around. The sub-classes (and thus the abilities you get) of Cleric are no longer based on the god you worship, but are now 'Hospitaler', 'Chevalier', 'Priest' and 'Missionary'. Do you feel that's a better system? If you think so... then fine. Your point is made, and I just disagree with it.