Dumas tells us right in the "Author's Preface," which is in reality a fictional frame to the story of the same sort Hawthorne made use of four years later in The Scarlet Letter (written between 1849 and 1850, published 1850). Dumas gives us their names with an interesting aside of speculation on their being pseudonyms of one sort or another:
D'Artagnan relates that on his first visit to M. de Treville, captain of the king's Musketeers, he met in the antechamber three young men, serving in the illustrious corps into which he was soliciting the honor of being received, bearing the names of Athos, Porthos, and Aramis.
We must confess these three strange names struck us; and it immediately occurred to us that they were but pseudonyms, ....
Hence, the names of the three Musketeers are Athos, Aramis, and Porthos. D'Artagnan, our hero and young adventurer, is not a Musketeer, although he is in Paris for the sole purpose of applying to become a Musketeer, and, during the course of his adventures, he does win that "illustrious" honor.
A "musketeer," in its simplest definition, is a soldier who carries and fights with a musket. A "musket" is a now antiquated form of firearm that has a gun powder chamber, loaded with powder and a lead shot, that is ignited when a steel-on-steel spark is transmitted to the chamber when the trigger is pulled. This is the firearm that the colonists in America fought with during the Revolutionary War for Independence.
More particularly and in relation to Dumas's story, "the King's Musketeers" were a small, select elite group of distinguished, expertly skilled, courageous (perhaps foolhardy) soldier musketeers who protected the King of France and answered only the the King's Captain of the Musketeers. From this we know that Aramis, Athos, and Porthos are three of the best warriors and marksmen of the most renowned courage and daring in France ... and ... D'Artagnan wants to be one of them. He will one day, in the chronology of the novel, be the fourth Musketeer: Athos, Aramis, Porthos and D'Artagnan!