The most common and most likely answer to this crossword clue is the 10 letter word REPUTATION
I've seen this crossword clue in The Daily Telegraph
R
E
P
U
T
A
T
I
O
N
Buddy explains!

The straight part
We know that "Name" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case name = reputation.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 REPUTATION mean?
REPUTATION noun- What somebody is known for.