As with most of the FMA characters, Arakawa has put deliberate thought into her characters' names. Roy's name is certainly no exception. Both his given name and his surname have a very particular meaning, that goes exceptionally well with Roy's personality and purpose in the series and which has a very particular symbolism.

First name: Roy.

A name which at first glance would seem a simple English name, with no purpose, it's exactly the contrary. From a French-English dictionary:
roi m 1. (souverain, a. dans les jeux) king

The name given to Mustang, whose ambition is to become the leader of Amestris is in fact the French word for "king". It's clear that Arakawa has Roy's quest quite known in her mind, and to be known by the readers.

Roy's surname, Mustang:

Such a name is part of a recurring trend from Arakawa. A good number of the military personnel's names and/or surnames have their origin in war air crafts and other military-related themes, objects, weapons etc (for example: Hawkeye, Havoc, and Fuery). Mustang is no different.

Within the Navy and Military, a "Mustang" is a term used for officers who have been promoted through the ranks through an in-service procurement program. The nickname for such officers is used as a compliment on their being able to rise through the ranks so quickly (as well as also being able to survive through the training/conditions thrown to them while in service).

P-51 Mustang:

The P-51 Mustang was a successful long range one-man fighter aircraft which entered service in the middle years of World War II, and its first flight in history was in 1941. The Mustang's combat record is generally considered to consist of 4950 air kills, 4131 ground kills and 230 V-1 kills. This airplane is considered by many to be one of the greatest war air crafts ever to be designed (some have gone as far as to say that it was the fighter plane that "won" the war).

In the Japanese version of FMA, Roy Mustang is written entirely with katakana, which is the alphabet used for with in western words (and also typically used by children before they learn hiragana and kanji).

Mustang, the horse:

Lastly, and probably the most amusing, is the Mustang horse. Mustangs were brought to America in the 1500s by the Spanish. They were used by Native Americans and the Spanish alike, and greatly changed the lives and warfare of the Natives. The name "mustang" comes from a Spanish word meaning "owner less or stray horses."

Writers tend to be methodical when choosing character names, and Arakawa's choosing of the name "Mustang" implies that Roy has the capability and will to put up a good fight against Bradley, and to attain his goal.