I first encountered it in
Hamlet: the first soliloquy, where
Hamlet is trying to make sense of his mother's second marriage, shortly after his father's death which she had mourned with apparent sincerity. And if you scan the lines,
A little month; or ere those shoes were old
With which she followed my poor father's body
Like
Niobe, all tears; — why she, even she,
then it's got to be NYE-ə-bee. I've got no clue what it would be in modern Greek, or indeed in ancient Greek, but I've never heard anything else.
The only name I pronounced spectacularly wrongly is
Heidi. I assumed that the -ei- would sound the same in
German as it does in Afrikaans, making it HAYdi, but of course it doesn't. It took a movie to disabuse me!