The original certificate remains available with the original details.
After the introduction of the adoption laws in 1930, a note was made on the original certificate that noted 'adoption', with no further details relating to the adoption.
After the court proceedings for adoption are completed, the child would have access to a short certificate under new adoptive name and parents. If you knew you were adopted, but not know who your birth parent/s were, you would need to apply to the courts for release of information and be directed to specialist adoptive services and units.
If you knew your original name, you would be able to order your original certificate without any problem. Many children don't have this info and therefore have to reach out for assistance.
This explains it much better than me!
www.nrscotland.gov.uk/research/research-guides/research-guides-a-z/adoption-recordsHowever, this doesn't apply for an informal adoption in the 1920s.
Monica