Both Uses of

epithet
in
The Bluest Eye

Marie seldom called Pecola the same thing twice, but invariably her epithets were fond ones chosen from menus and dishes that were forever uppermost in her mind.†
Chpt 2 *

Definitions:

(1) (epithet as in: racial epithet)
an insulting or abusive word or phrase
(2) (epithet as in: earned the epithet, "The Great")
a descriptor added to a person's name -- as in Alexander The Great

or:

a phrase used in place of a name or word -- such as: The Big Apple for New York, The Great Emancipator for Abraham Lincoln, or man's best friend for dog
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

In botany, a specific epithet or epithet is the word identifying the species.