The initials in H. M. Murdock are backronymed 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?
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.