My question is: How common was it in the late 1980s - the character was born around then - and in a domestic adoption, for an infant (six months old at the time), to be given a new name by their adoptive parents?
It'd also be helpful, although not strictly necessary, to know what kind of change, if any, there's been in this statistic between then and now.
ETA: So it's common (actually, seems to be more common than leaving it alone, judging by the near-unanimity of the affirmative responses). Got it. I think the reason I needed to ask was that somehow I'd ended up with the idea that open adoptions (which are commoner and commoner these days) = keep the original name.