What does it say on your father's birth certificate. What name does it say for his father?
There are lots of possibilities as to why his father went to live with someone else when he was young. Maybe his mother had him illegitimately when she was young and couldnt afford to keep him, so the other couple took him to save her name. She then may have married somebody or lived with someone called Hibbert and the subsequent children were named after him. Later on Cecil could have returned to his mother and used the name Hibbert. Its all surmising of course but a possibility.
If you find his birth in the actual parish registers, it should give his mother and fathers name which will be a start.
Good luck.
Kind regards
Hoppity