Why is he called the 'Adventurer'? He's a Warrior class, thus he should be named appropriately.
Adventurer makes no sense.
He is tagged for his class, he's just also got his own tag for being the iconic character. (This also allows him to be tagged appropriately if someone depicted him in dragoon armor, as he appears at the end of the Heavensward opening cinematic.)
"Adventurer", however, does make sense in its own right. In Eorzea, "adventurer" is a career path of sorts - soldier-of-fortune, itinerant do-gooder, anyone who wanders around using their skills on the local tasks-at-hand (i.e. quests) to support themselves rather than stay in one place and build a business or join an organized military company.
That said, "Warrior of Light" would be a reasonable alternative tag name, or perhaps warrior_of_light_(ff14).