There were two ways that patronymic (“son of”) surnames were rendered in Wales; firstly the “Dewi ap Gwilym” form that you mention (more common up to the 1600s) and the anglicised “David Williams, son of William Lewis” that was probably restricted to official records (due to the parish records being written often by monoglot English officials).
The fixing of surnames was a gradual process, starting with the upper classes and being complete in the middle of the 19th century with the advent of extensive record-keeping in all areas of life.
Since surviving records are typically official ones, the recorded names generally transition between the old “ap” form to the anglicised form to a fixed surname. However, it's interesting that Morgan has a typically Welsh surname (Gwilym = William) so it's likely the surname that he used in day-to-day life rather than the surname found in official (anglicised) records. As such I'm inclined to believe it to be a patronymic surname, and that Gwilym was his father's forename. However, if one were to search for him in official records in Wales, you'd likely find him under “Morgan Williams” or “Morgan William”.
Incidentally “Cevmaman” is almost certainly a mistranscription; no place exists of that name. I would guess it to be Cwmaman, or possibly Cefnaman (if such a place exists; I can only find a farm of that name in northern Wales so not likely relevant to Morgan).