Opposite of an eponym

What is it called when someone lives up to their name. Their name is Smith and they become one for example.

Solution 1:

"Nominative determinism is the hypothesis that people tend to gravitate towards areas of work that fit their name. It predicts, for example, that because of their names, the scientists Splatt and Weedon ended up as urologists."

https://en.wikipedia.org/wiki/Nominative_determinism

Solution 2:

You might consider the neologism Aptonym

aptonym ‎(plural aptonyms) A proper name that aptly describes the occupation or character of the person, especially by coincidence.