self-insert

Short definition from Wiktionary

Noun

1. 1
   A character in a story who represents the author's own person.
2. 2
   A character in a story who the reader/viewer is meant to identify with.

Verb

1. 1
   To insert oneself.
2. 2
   To insert something into one's own body.
3. 3
   To insert one's own person into a story as a character.