A word that means "to become one's name"
I'm looking for a word which indicates that a person has adopted a quality suggested by their name, e.g. a person named Grace who is indeed graceful, or perhaps someone named Shepherd who has become a shepherd.
I have a strong notion that I once learned such a word, but I have forgotten it and have never re-discovered it.
Aptronym
An aptronym, aptonym, or euonym is a personal name aptly or peculiarly suited to its owner.
[Wikipedia]
I believe you may be thinking of Nominative determinism, a theory which describes a phenomenon where somebody's name significantly influences their job, status or personality.