There are examples of hermaphrodite humans, but this is a malfunction of the foetus, and either one, or both of the sets of reproductive organs will not function properly.
One of the most famous (and unfounded!) rumours is that Hollywood actress Jamie Lee Curtis was born an hermaphrodite - although the preferred modern term is 'intersexual'.
The rumour started because she was christened Jamie Lee - which rumour monger saw as an amiguous name suiting a child of either gender, until surgery was performed to make her female.
The actual explanation is far more simple - but not as gossip-worthy.
Jamie Lee's parents, film stars Tony Curtis and Janet Leigh chose Jamie's name before she was born, so that which ever sex their baby was, the name would fit.
Quite why Jamie's elder sister, Kelly Lee, whose name was also chosen before her birth with the same intention and for the same reason, escaped this ludicrous apocryphal story is maybe due to her not being as famous as her younger sister.
Hollywood eh? What are they like!