The most common and most likely answer to this crossword clue is the 6 letter word SELVES
I've seen this crossword clue in The Guardian
S
E
L
V
E
S
More clues leading to the result SELVES
Buddy explains!

The straight part
We know that "The real me and others" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the real me and others = selves.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 SELVES mean?
SELVES noun- One individual's personality, character, demeanor, or disposition.
- The subject of one's own experience of phenomena: perception, emotions, thoughts.
- An individual person as the object of his own reflective consciousness (plural selves).
- Self-interest or personal advantage.
- Identity or personality.
- A seedling produced by self-pollination (plural selfs).
- A flower having its colour uniform as opposed to variegated.
- Any molecule, cell, or tissue of an organism's own (belonging to the self), as opposed to a foreign (nonself) molecule, cell, or tissue (for example, infective, allogenic, or xenogenic).