In the Chinese theory, it stems from either “kôe-chiap” or “kê-chiap”, both from the Amoy dialect, where it means “the brine of pickled fish or shellfish.”

from http://masterblog.front.lv/category/fun/

As for the “eggplant sauce” theory, ”ketchup” derives from a Chinese word composed of two characters (茄汁), which means “eggplant sauce”. The first character (茄), meaning “eggplant”, is also the root for the word “tomato” and the second character (汁) means “juice” or “sauce.”

The Malay theory states that the English word originates from the Malay word kicap (or, kecap, ketjap), which translates to “fish sauce” – which is borrowed from the Chinese, anyway…

European-Arabic Theory:  E.N. Anderson, an American anthropologist, claimed that ketchup comes from the French escaveche, meaning “food in sauce”  (imagine… French ketchup!) while culinary historian Karen Hess traced it back to Arabic iskebey, or “pickling with vinegar”.

Blue Label Ketchup 1898, from wiki article