pet name 
noun
A name that is used instead of someone’s usual first name to express fondness or familiarity.And ‘Pinky’ is a name (more of a pet name, really) that both men and women choose or are given....
- ‘Hey there, Munchausen,’ he said quietly, calling her by an old pet name.
- Johnny calls Francie ‘prima donna’ as a little pet name.
Synonyms
affectionate name, term of endearment, endearment, nickname, diminutive
rare hypocorism, hypocoristic