Translation:My last name is Wang.
姓 (xìng) is not a noun for "surname/last name", it is actually a verb meaning "to be surnamed". The sentence is literally "I am surnamed Wang." Here, it is easy to see there is no possessive in the sentence. But in English, we don't typically use the verb "to be surnamed"; our loose English translation presents with a possessive instead (MY last name is Wang).
i would like to point out that contrary of western culture, our family name(Surname) comes first followed by our given name. For example Will Smith. Will (Given Name) Smith (Surname). Since this is Chinese, I'll give a Chinese Example. Lee Wang Yu. Lee (Surname) Wang Yu (Given Name)
There are several colloquialisms that translate and Duolingo can only mark it right if they considered it ahead of time. They also phrase the lesson in the same manner several times giving you all the clues you need if getting each answer correct each time is important to you. I am trying to learn a language not get the high score.