From experience, children who were adopted out of their birth families as young babies tended to have their names changed to ones chosen by their adoptive parents.
If the child was adopted at a slightly older age and knew what their name was, then the chances are that the birth name was kept.
There are plenty of topics here on finding adopted people, although there is also the chance that if she was adopted as a baby, may not know she was adopted. Way back when, the subject of adoption was extremely sensitive to all parties, it's only over the years that attitudes have changed and adoptions are more frequently talked about.
If you do not have her name after adoption, then it will be almost impossible to find her.
I suggest you start by putting your name on one or more contact registers, this is the link to the GRO
https://www.gov.uk/adoption-records/the-adoption-contact-registerIf you also google search 'adoption contact register' you will find several other places where you can register to be contacted.
Unless the name you are looking for was unbelievably rare, then the person you found just might be someone totally unrelated.