I'm not a user myself, but tomato ketchup / catsup is a popular in China, too. Not really surprising given its history; it probably originated here, albeit in a very different form.
In Chinese, it is either 番茄沙司 (fān qié shā sī) or S: 番茄酱; T: 番茄醬 (fān qié jiàng). Both names use 番茄 (fān qié) to mean tomato but the literally meaning is 'barbarian egg plant' due to them being American in origin.
Dictionary.com expresses its mystification as to why eggplant. Simple really. Tomatoes and eggplants are part of the same botanical family Solanum.
A common alternative name for tomatoes is S: 西红柿; T: 西紅柿 (xī hóng shì), literally 'western red persimmon'. Despite the visual similarity, persimmons and tomatoes are unrelated. Dictionary.com doesn't query that. Amateurs.
Heinz ketchup is widely available
but, of course, there are numerous local brands, too.
Also McCormick have their take on offer.
Besides being used as a dip for fries in American and American style fast food places, tomato ketchup is often used as a cooking ingredient in sauces and even hotpots.
