Can you explain why Haitians say 'pou lèzentim' when they tell you their names?

pou lèzentim (from French pour les intimes) → for close / intimate friends.

They are letting you know what their nickname is.
pou lèzentim indicates what your close friends call you.

examples:

Mwen rele Jean Broullard, Janjan pou lèzentim.
I'm called Jean Brouillard, and it's Janjan for close friends.
My name is Jean Brouillard, my friends call me Janjan.

Non mwen se Felix, Fefe pou lèzentim.
My name is Felix, and it's Fefe for close friends.
My name is Felix, my friends call me Fefe.
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words