In principle, under what circumstances is it "OK" or even "preferable" that a child be deprived of his biological father's identity? And going forward, should we compel the sharing of his identity in those circumstances anyway? Or perhaps we should just do our best to end those kinds of circumstances in the first place.
I think about half of who we are comes from our biological heritage. That is important for a person to know. And I am impressed with how very much adopted kids and donor kids want to know who their natural parents are. So, I would incline to have open adoption and donation.
But requiring it by law in all cases? That seems to be too much.
Perhaps a market solution -- you pay extra for secrecy? Or a judicial bypass -- you can keep it secret if you can convince a judge that you have a good reason? Let each state make its own rules democratically, knowing they would differ from one another?
If the law had a presumption of openness, with some rational possibility of an exception, seems to me to be a centrist solution.
Addendum: I was chided on the above answer as inadequate and not really principled (see the first comment below). I thus add this explication.
The principle that I am applying is that principles establish a general rule, to which there might, in principle, be exceptions. The principle that applies is that law should support the presumption that children should know who their parents are. But in a wild and varied world, situations might arise that no one, myself included, can predict that would produce a good reason for secrecy. Hard cases make bad law, so we should tailor the law to the general principle, not the hard case.
Thus I believe the best we can do is to provide a general structure of openness, with known, open, and legitimate means to create exceptions.
As I said at the outset of this discussion I don't think identity comes from any one or absolute source, including biology. Biology is always important to our bodies, of course, and is almost always important to our identities, but it is not of overriding importance; it is one factor among other, and the mix of factors differs from culture to culture and person to person.
Moreover, however you conceive of identity, I don't think you have a legal and universal "right" to identity.