The initials in H. M. Murdock are backronym to "Howling Mad" but that is clearly not his actual given name. Wikipedia (see link) only states several occasions where his name was not revealed.
What is his full name?
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His name is never revealed, although according to the A-Team Wikia, the 2010 movie suggests that his first name is James. Furthermore, in S3E18 ("Road Games"), Hannibal calls Murdock 'Henry.'
Despite these allusions to his real name, it is never definitively stated.
the initials H.M. were never explained in terms of what Murdock's actual first and middle name were, and the nickname "Howlin' Mad" were simply attributed to them (although it is rumored that his name comes from World War II Marine Corps General Holland M. Smith, aka "Howlin' Mad", a nickname given by his troops). Not even his driver's license reveals what "H.M" stands for.
The Episode showed the rumor that the H.M. 'Howlin Mad' nickname came from Holland M. Smith. Apart from that, no other explanation of his name have ever been given.
I think it's Henry Mack. As stated by the previous poster, at one point, Hannibal calls him Henry. Also, in season 2 episode 14, Murdock refers to himself as "Mack Murdock". Henry Mack "Howling Mad" Murdock.
Actually, in the first episode his first name was revealed as being Harry Mack Murdock. It was revealed during the original first airing of that episode. All subsequent playing, including re-runs, VHS copies and DVD copies since that time have shown the edited version of the original source tape. It has never been explained why this was done, and the reasons are unknown.