Actually this goes all the way back to FFII (Official version not the American travesty) where the first Dragoon is introduced in the series by the name of Ricard Highwind who was the last Dragoon left after the Palamecian Empire wiped out his clan and poisoned their dragons.
Highwind is thus a running gag in the series always associated with Dragoons with both Kain Highwind and Cid Highwind being future Dragoons in the series. Kain is also immortalized, since he's the most famous dragoon, by having a weapon named after him called Kain's Lance which debuted in FFIX and has appeared in the Tactics Advance series as well as FFXIII. Speaking of XIII, Fang, the game's token Dragoon character, has a special ability that looks like the classic Dragoon jump ability and its conveniently called Highwind.The only exemption of the Highwind name in the series is the King of Tycoon whose full name is Alexander Highwind Tycoon according to art books and source books.
Another name that gets around is Leonheart. Its the full name of Leon in FFII who became the series first Dark Knight. Funny enough, according to the Settei Shiryou Hen (an early Japanese source book before FF switched over to the Ultimania collections starting with FFVIII) the Deathbringer sword that Cecil obtains in Fabul in FFIV actually has a backstory which stated the sword used to belong to a Dark Knight who came upon Fabul when he was injured, he was so grateful and impressed by the monks that he renounced the sword and became a monk as well. His name according to the Fabul Legend? Leonheart.
An odd coincidence of naming comes from the EV of FFVI where Tina is renamed Terra which ends up creating another contrast to the other main heroine of the game Celes. Terra is another name for Earth while Celes can be interpreted as being short for Celestial or Heaven. I don't think Woosely had that in mind when he changed Tina's name (course he may have but never mentioned it). A similar contrast is in FFVII between Cloud and Aerith who once again use the Heaven and Earth naming schemes. Course this goes on forever with Nomura's titles since he loves naming his protagonists after celestial bodies or weather effects: Cloud, Squall, Tidus, Yuna, Sora, Lightning, Snow, Noctis... etc....
Another amusing contrast between names is between Cloud and Zack. Cloud's last name being Strife, Nomura decided to make Zack's last name contrast it by making his last name be Fair.