The most common and most likely answer to this crossword clue is the 8 letter word NICKNAME
I've seen this crossword clue in The Daily Telegraph
N
I
C
K
N
A
M
E
More clues leading to the result NICKNAME
- Wormwood Scrubs, perhaps — or what it’s familiarly known by?
- How to impersonate Mephisto?
- After prison chap returned with Eastern alias
- The Devil’s title, commonly?
- Monica heard Nikki?
- Tiny cut by music publication about a term for someone
- Soubriquet
- Davy Jones, maybe?
- Jug fellow lifted with base and handle
- Arrest European holding guy up in the Big Apple, for instance
Buddy explains!

The straight part
We know that "Identity given" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case identity given = nickname.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 NICKNAME mean?
NICKNAME noun- A familiar, invented given name for a person or thing used instead of the actual name of the person or thing.
- A kind of byname that describes a person by a characteristic of that person.
- To give a nickname to (a person or thing).