The most common and most likely answer to this crossword clue is the 6 letter word NITWIT
I've seen this crossword clue in The Daily Telegraph
N
I
T
W
I
T
More clues leading to the result NITWIT
- Up in time, shortly accompanied by fool
- Fool can in turn with comedian
- Name one foolish person, then another
- Idiot in retired nincompoop
- Fool North with one trump initially, then with 22 being discarded
- Idiot returned money with reduction
- Idiot Trump initiative world leaders can reverse
- Doin’ it without holding ass
- Name one silly billy or another
- One idiot upsetting home with another
Buddy explains!

The straight part
We know that "Name given to one fool? Yes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case name given to one fool? yes = nitwit.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 NITWIT mean?
NITWIT noun- A scatterbrained or stupid person.