The most common and most likely answer to this crossword clue is the 5 letter word NOMEN
I've seen this crossword clue in The Guardian
N
O
M
E
N
Buddy explains!
The straight part
We know that "First part of Julius Caesar, for example" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case first part of julius caesar, for example = nomen.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 NOMEN mean?
NOMEN noun- The name of a citizen of Ancient Rome, designating them as a member of a gens.
- The birth name of a pharaoh, the fifth of the five names of the royal titulary, traditionally encircled by a cartouche and preceded by the title zꜣ-rꜥ.