The most common and most likely answer to this crossword clue is the 8 plus 4 letter word IDENTITY DISC
I
D
E
N
T
I
T
Y
D
I
S
C
Buddy explains!
The straight part
We know that "Personal tag" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case personal tag = identity disc.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.