It means "of" or "from" Artagnan, a town in the southwest French district of Hautes Pyrenees. It's not a first name as such, but more of a last name or honorific like "von Richthofen". It may denote minor nobility, a class of people who didn't easily descend to the familiarity of first names in everyday social relationships.
The specific source for D'Artagnan was apparently Charles de Batz-Castelmore d'Artagnan, a French soldier of the early 1600's whose memoirs supposedly were used by Dumas as a basis for "The Three Musketeers" and other works.
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