The most common and most likely answer to this crossword clue is the 8 letter word SURNAMES
S
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N
A
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Buddy explains!

The straight part
We know that "family identities" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case family identities = surnames.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 SURNAMES mean?
SURNAMES noun- An additional name, particularly those derived from a birthplace, quality, or achievement; an epithet.
- An additional name given to a person, place, or thing; a byname or nickname.
- The name a person shares with other members of that person's family, distinguished from that person's given name or names; a family name.
- (Classical studies) The cognomen of Roman names.
- A clan.
- To give a surname to.
- To call by a surname.