Roy (Mustang)- Of Celtic/Gaelic heiritage, it is likely derived from the Gaelic word "ruadh", meaning "red". A "notable bearer was Rob Roy, a Scottish outlaw of the 18th century." However, the word itself is identical to the french word "roi", which means "king". So Flame's name could be possibly translated as "Red King" or "Red Horse" (if we take into account the "Mustang" portion of the name). This hold somewhat ominious connotations - to be sure, Roy is a "Red King" - he's a war hero of the Isbal Massacre, and has admitted that he is "drenched in the blood of those he has slain". In this meaning, Roy is both the king of the dead or a king who is liberally drapped in the blood of the slain - recall both his desire to become Furher and Hughes' sacrifice, which weighed heavily on him.
Riza (Lisa) Hawkeye - A possible derivation of "Elizabeth", the name is drawn from the Hebrew name Elisheba, meaning "my God is an oath", "my God is abundance", or "consecreted to God". The name of the mother of John the baptist, it was also the name of a ruling queen of England (Queen Elizabth) and an Empress of Russia. Seems to fit her somewhat - she is fanatically loyal to the few she places her trust in.
Maes (Hughes) - I was unable to locate the name by the official spelling given. The closest match to be found was "Maas" - a short form of Thomas. The name "Thomas" is derived from the Aramaic name "Te'oma" which means "twin" - in the New Testament, the name of the apostle who doubted the resurrected Jesus (who was, incedentally, martyred). While not apparently fitting to this character, I find it oddly suitable for Hughes - he is, after all, Roy "brother", kin in all but blood.
Alex Louis (Armstrong) - "Alex" is a shortened form of the greek name Alexandros which meant "defending men" or "protector of mankind". It also may tie back to one of the names of Apollo - greek god of light and the sun, whose titles inculded "averter/destroyer of evil". He had a long list of duties - in addition to being known as the sun god, he was also the god of prophecy, medicine, music, art, law, beauty, and wisdom. "Louis" - ultimatly derived from the Germanic name Hludwig, meaning "famous warrior". Add to the various definitions the surname - Armstrong - and you get a name which means something alsong the line of "Famously strong warrior who is a protector of mankind". (I can just picture Armstrong bellowing that out and posing.)
Jean (Havoc) - French derivation of the name "John", which is, ultimately, derived from the Hebrew name Yochanan, meaning "God is gracious". A common name, it is shared with several highly revered saints, at least 23 popes, and a number of kings and poets. I suppose the name's meaning could be crammed down into "gift" or "gifted" - in which case, the addition of the surname "Havoc" could cause it to be (roughly) translated as "a gift of chaos".
Cain (Fury) - A Hewbrew name, it's defintion can be described as "craftsman" or "acquired". Somewhat more ominously, it is also the name of Adam and Eve's firstborn, spelled here as Caine - the first murderer, kinslayer, who killed his brother Abel out of a fit of jealously. (On a random note, various legends state that the original Caine was cursed with immortality of some kind - various myths hold that he became the first vampire). So the name itself holds the ominous meanings of "Aquired Rage", and is associated with homicide. Not very fitting to the Fury we know from FMA.
Vato (Farman) - I was unable to find an exact match for this name - the closest I could find was the name "Vito", a Roman/Italian derivation of the word "Vita", which literally means "life". The name "Farman" is actually far more interesting. Far - distant, the opposite of close, calling to mind horizons and mysteries. Man - man. So the name in question can be losely translated as "A Distant Life".
Heymans (Brenda) - The name Heymans was absent in each and every one of the various name dictionaries I paged through. The only name vaguely associated with it in any way was "Heydar", an iranian verions of the name "Haidar". "Heidar apparently means "lion" in Arabic - a basic, fairly standard name. No riddles, no real interior meanings. Save for the rather humorous comparison of the FMA character's aversion to absolutly anything of an animal nature. Brenda is loyal, and fairly trustworthy - while he is given a chance to shine in the manga, he is fairly absent in the anime.
If you want me to, I'll continue my name definitions with the rest of the characters.