children living with parent, with different surname

Let’s say a child lives with a mom, but does not have the same surname as the mom. And the mom is not the head of household.

Would this child look like they are not living with any of his/her parents?

Not necessarily. The RELATEvariable identifies the stated inter-household relationship status of individuals within census data. Values for this variable come directly from the response given on the questionnaire form. In fact, even more complicated family interrelationship variables don’t rely on surnames to identify family relationships.

I hope this is helpful.