If I was talking about my family, then I would say "Our last name is Lewis."

If I happened to be with a bunch of people, who were not related to me but happened to also have Lewis as their last names, I would want to say "Our last names are Lewis"

no.

it would not work because Our last names are wang would mean like i met this guy and his last name was also wang. but what i did for my answer ( which is actually very close ) was our last name is wang as if you meet somebody and then you get into a conversation and then the person you meet says that their last name was for example Lee and then you say your last name was Wang. but then again,it would have to mean that you have more than 1 person with you that has the last name Wang.

I wouldn't be correct since it's grammar doesn't make sense

I thought the same thing at first. After some research I found out that 姓 is actually a verb meaning 'to be surnamed' or 'to have the surname' so what you're really saying here is "We are surnamed Wang". So in this case, you don't need 的 because you don't really want to say "Our are surnamed Wang".

You can omit de as a possessive (it's optional) if it's something personal, like "my mom" could be written as wo mama

I've noticed that Duo prefers us to follow the order closest to what is on the page even when the meaning is similar.

I have never heard anyone say “We are surnamed ....” or “I am surnamed ...”

Try to use natural English translation when learning another language rather than a literal translation.

Wang is technically the family name, which is our last name. Translating 姓 to English becomes "Our last name is Wang."

English people use last name but the chinese use Surname or Family name and for first name they says Given name

No. Some of the other translations on this thread sound odd, but, "We are of Wang" just makes no sense in English.

Either 我们姓王 (姓 used as a verb) or 我们的姓是王 (姓 used as a noun)

No, 我们 is we, not I.