Sorry, there is no straight forward answer to this. Anglican Church registers sometimes wrote an anglicised name in the register when the family would have continued to use the patronymic name. There are fervent Welsh nationalists who choose to be known by their patronymic today. Yes, the ap Hyw became Pugh, the ap Rytherch became Prytherch, or even Protheroe; but the biggest change was the pluralisation of the possessive case. Efan’s became Evans, Robert’s became Roberts, John’s became Jones, Hyw’s became Hughes. These were people aspiring to get the benefits of anglicisation.
Even in my youth, there were nicknames. Albi Du was the coalman. Roughly translated as Black Albert. In ancient times his son Dafydd would have been Dafydd ap Albi Du to distinguish him from other Dafydd ap Albi.
Not a very helpful answer but I hope informative.
Steve