He was never given in a name in the show. However, according to a 2010 interview he was referred to as "Samuel" internally. Unfortunately I've been unable to find the interview itself1, but the fact was reported by many film and television blogs of the time; SlashFilm, for example:
[F]or those of you Lost fanatics, we finally have confirmed the man in black’s official human character name. After the jump.
His name is…
ready for it?
are you sure?
A bit anticlimactic, right?
We actually already knew of this name as it was featured on the casting call for “The Incident” (the first appearance of the man in black, in which he was credited in the final credits as simply “Man #2″).
The name also featured in the auction catalog for actor Titus Welliver's on-set chairback:
An email from Gregg Nations, a script coordinator on the show, to the Lostpedia fan wiki, somewhat contradicts this; according to Nations, "Samuel" was never intended to be the character's actual name, but was rather just something made up for the casting call2:
Who knows why production used "Samuel" as opposed to "Man in Black" for the chairback. Titus didn't know his character's name since he never was named, and he may have told someone in production the name used for the casting breakdown and sides. (The breakdown also listed him as a corporate raider, and that obviously isn't what his true job was.) But it's just a placeholder name and was never meant to his real name.
On a less serious note, a "deleted scene" shown at SDCC 2011 reveals that his name is Barry. Apparently he's sensitive about it:
1 Articles of the time reference an E! Online article, but the page as been removed and I haven't been able to recover the video through the Wayback Machine
2 Thanks to NikolaiDante for pointing this out