"Our last name is Wang."
It's nearly the same, 我的will make 姓a noun, and 我姓will make 姓a verb. My surname is... And I'm "surnamed "... Which is more used :)
I think the sentence is about a family, so it's one shared name. But you could be right if they are from different families (it's a very common name).
Is it wrong to say 我们姓是王 because 姓 functions as the verb making the copula, 是, obsolete?