One situation I found from the late 1800's illustrates the difference in adoption procedures then & now in the USA. Three little girls ages 9, 7 & 6 were orphaned. They were taken in by three different families in the area. The eldest was formally adopted by a non-related family, but kept her birth name, according to the census information. The middle girl was raised by her father's sister & her husband, but never adopted. The youngest was adopted by a widower, also non-related.
Modern adoptions seem to have a fixation on anonymity... That's where the "erasure" of the birth name originates. Prior to that, keeping the birth name was the norm.