technically they are called aubergines and eggplants, but saying 'aubergine' gives blanks stares anywhere I've been in North America. As a designer I love fancying up eggplant dishes on restaurant menus with 'aubergine' in the name if they'll let me, and then still include the word 'eggplant' in the description of the dish for those who aren't aware of the meaning.
Yes, I was merely pointing out that Darwin's children (being British) would not have called it an 'Egg Plant'.