If I'm understanding you correctly, are you asking whether parents are required to tell their adoptive children that they are adopted? In the US definitely not, and I think that's probably the case most places.

Whether or not the parents had a paternity test performed wouldn't have any bearing on it.

This isn't necessarily a bad thing—studies[1] have shown that adoption discovery between birth and two years of age may increase life satisfaction and decrease stress.

The same applies to other cases where parents aren't genetically related to their children (i.e., donor egg and/or sperm).

[1] https://www.theatlantic.com/family/archive/2019/07/adoption-...