The Mark of Name
Kain is clearly a derivitive of "Cain". There is no name Kain, but Cain has several meanings attached to it. Whether Square decided to go with an alternative spelling because of the intense censorship placed on their games at the time of Final Fantasy IV's first US release (remember, they removed names like "Holy" and the command "Pray"), or they decided that Kain just looked cooler, or both, is unknown. However, if they wanted to change the official name to "Cain", as it is spelled in several fan translations, they have had several opportunities, as the game has been rereleased several times. (And consider that more recently Square has moved towards using Aerith instead of Aeris, for example.) Thus, I accept Kain as the official English translation- it sounds exactly the same as Cain anyway. (Let it be noted that several videogames have followed suit with the name Kain.)
The word cain is hebrew for spear. We see how this is releveant, as a dragoon's primary weapon is a spear, though he can equip swords and axes as well, we know what he's really about. Even beyond the biblical imagery, that's an obvious reason for this name.
But really, the biblical story of Cain and Abel is why we're here. Cain is the older brother of Abel, the son of Adam and Eve. While his brother raises sheep, Cain tills the earth. They both bring an offering before the Lord, but Cain's is found unworthy. I quote now from the King James Version, Genesis 4.6-10:
And the LORD said unto Cain, Why art thou wroth? and why is thy countenance fallen? If thou doest well, shalt thou not be accepted? and if thou doest not well, sin lieth at the door. And unto thee shall his desire, and thou shalt rule over him. And Cain talked with Abel his brother: and it came to pass, when they were in the field, that Cain rose up against Abel his brother, and slew him. And the LORD said unto Cain, Where is Abel thy brother? And he said, I know not: am I my brother's keeper? And he said, What hast thou done? the voice of thy brother's blood crieth unto me from the ground.
It is true that Kain and Cecil are not blood brothers, but they were raised as such. And, more to the point, Cecil does have a brother out to destroy him all the same. Kain's jealousy of Cecil and his desire to prove himself greater than him, even in attaining honorable goals, is easily manipulated towards evil. This is stressed in the biblical story.
But Cain's biblical character is a bit more complex than that-- there is more to his story. He is cursed, and forced to wander the world, unable to practice his former vocation. Genesis 4.13-15:
And Cain said unto the LORD, My punishment is greater than I can bear. Behold, thou hast driven me out this day from the face of the earth; and from thy face shall I be hid; and I shall be a fugitive and a vagabond in the earth; and it shall come to pass, that every one that findeth me shall slay me. And the LORD said unto him, Therefore whosoever slayeth Cain, vengeance shall be taken on him sevenfold. And the LORD set a mark upon Cain, lest any finding him should kill him.
The mark of Cain is one not of forgiveness, exactly, but contemplation. God marks Cain as His own, despite his shortcomings. Cain is given time to repent, to learn to ask foriveness and perhaps eventually to recieve it.
It should be noted that in Final Fantasy IV Advanced, Kain's ultimate weapon is the Abel Lance. (This being an upgrade from the Holy Lance, but both weapons have decidedly spiritual qualities.) This may be an indication of his redemption, that he has conquered his jealousy and tamed the fickle part of his nature.
The name Highwind is fraught with mythology of a different kind. While FFOnline has suggested that the name Highwind has been given to characters who are fundamentally alone, it's easier to argue that it's simply been given to dragoons. Richard Highwind of Final Fantasy II is a dragoon, King Tycoon from Final Fantasy V was a dragoon at some time in his past, and Cid Highwind from Final Fantasy VII, though not a dragoon proper, has the spears and the jumping attacks. As Kain himself mentions, a dragoon's strength is fighting in the air- Highwind is a fitting surname for such a fighter.