It's a long shot, but I have some of my family with a very similar name. My great X2 grandfather was a Rice Williams. He was from Amlwch in Anglesey. He married several times, and on at least one marriage certificate he stated his father was an Edward Stockley, and on another Edward Williams. His siblings mostly seem to be known as Stockley, although one is a William Williams Stockley.
His father Edward Williams Stockley also seemed to use the two names interchangeably. On his death certificate he was Edward Stockley and on the last marriage certificate (he married 3 times, only once after 1837) he was Edward Williams. His father he stated was a William Edward (an example of Welsh patronymics). Censuses again show the two names as being interchangeable. A contemporary diary records Edward Williams Stockley's death naming him as Edward Stockla, and another source talks about him as Stockley's man, but we have no idea who this Stockley might be. Have you made any progress in finding out why your family was called Williams Stockley?
Thank you for any help
Rhiannon