The eldest son of my great grandfather was named Robert Roberts Roberts on his birth certificate, which is even more puzzling, although I have found another Robert Roberts (Williams) elsewhere.
Most of us born in Wales or England before the mid 1970' s don't have a family name / surname on our birth certificates. My birth certificate says that I am a boy named Alwyn and that my father is Hugh Humphreys; Humphreys as my surname is just assumed from my father's surname. When I asked a solicitor about changing my name to Alwyn ap Huw by deed poll in the 1980's he told me that it was unnecessary because "ap Huw" can equally be assumed from my birth certificate.
Fixed family names in Wales were first used in the 1500's after the acts of union, but didn't become a fixture throughout Wales in all classes of society until the about the 1890's (and by then members of the new cultural nationalist movement who had fixed surnames began reverting back to the more traditional patronymic form -Ifan ab Owen Edwards, for example).
In the cases of both your Robert Roberts Roberts and Robert Roberts Williams, what you have is the parents using the given name section of the birth certificate to state what they want the child's surname to be; Robert Williams want's his son to be known as Robert Roberts (Robart ap Robart) NOT Robert Williams. Robert Roberts Roberts is telling the registrar that his son is not just Roberts because he is the son of Robert, but also because he is the grandson of Robert (Robart ap Robart ap Robart).
Sorry if this sounds confusing, Welsh naming is a bit like tying shoe laces; something you can do without thinking if you know how, but is almost impossible to describe how to do to another person; which is why I recommended John and Sheila Rowlands book in my last post.
