The most common and most likely answer to this crossword clue is the 3 letter word NED
I've seen this crossword clue in The Times
N
E
D
Buddy explains!

The straight part
We know that "Name of man" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case name of man = ned.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does NED mean?
NED noun- A person, usually a youth, of low social standing and education, a violent disposition and with a particular style of dress (typically sportswear or Burberry), speech and behaviour.