Hi Marion,
Just trawling through to see if there were any questions
that I could answer and noticed your query.
No, there was no formal or legal adoption procedure in the early 1800s. It was as you thought; the children might take the step-father's name without any adoption.
In the 19th c., it is common to see children appearing in census records with the step-father's surname, only to appear in later records such as marriage certs with their original names. Once they grew up, some seem to have chosen to be known by their real father's name, but in your case it seems that they used the step-father's name on their marriage certs.
Are you searching for the original name of these girls?
If so and you don't know the mother's previous married name, try looking for her second marriage under the second husband's name. Unless there was another man with the same name, it should be fairly easy to spot. Once you have her first married name, you should be able to find the first marriage and the girls' baptisms in the PRs.
I also have Wing ancestors. One of my families lived there for over 300 years. The name is Woodman, with
connections to many other Wing families.
Cheers,
Carmela