Appears Miss Lamb's children went by their father's surname and not the name they were registered with at birth.
This is normal practice.
An illegitimate birth can only be registered in the father's name if he accompanies the mother to the registrar's office and signs the certificate at the same time as she does.
A corrected entry can be made if the father's name is determined in a court case for paternity.
However even if the child is not registered in its father's name, everyone in the parish probably knows who the father was, and the child will turn up in the census etc under its father's name.
The important thing to know is the
parish[/b] where something occurred. The county is useful, but as you have found there can be places with the same names in different parishes, and even, occasionally, there could be more than one in the same parish.
It is possible that the kirk session might have taken an interest in Miss Lamb's pregnancies, in which case there may be some record in the minutes, if they have survived. If so, they would be in the National Archives of Scotland, but they are not available online.
It's also possible that the parochial board records might have some record, if she applied to the parish for relief. These records, if they have survived, will be in the Aberdeen City Archives, and there will be a microfilm copy in the Moray Local Heritage Centre in Elgin. Try
http://libindx.moray.gov.uk/mainmenu.asp - you never know.
