Take a look at GenUKI "Civil Registration" which provides a good overview of the historical and legal requirements for Civil Registration in the UK. You will note from the information that it was not compulsory to register births until 1875 and a 6 week requirement for registration was made. Issues such as illegitimate births, poor standards of literacy, immigration, religion and other factors all contributed to making early registration from 1837 often a complex affair when tracking down ancestors. It maybe that there is no civil registration for your ancestor and any name change only complicates the matter. With regard to the need to have proof of birth this would not apply to most people even when marrying ( some of my distant relatives had alias when marrying and gave false information due to prior criminal backgrounds and other issues) and factors such as travelling abroad or making wills etc was not wide spread.
Phillip