His initials are clear to see and represent the Christian names William and John. The answer was no, because for the first 12 years of service, he was recorded as John Dedman and some nine months after he had signed on to complete his pension time the Admiralty changed his Service Certificate [SC's] to read William John.
However, he was always called Jack throughout his life by all comers [family, friends and acquaintances] but not [obviously] by officialdom. In this picture above, you can clearly see that the name William has been added in before the word John.
In fact, the lesson told by guest Abstract Rude pretty much certifies that the song is a fable rather than an autobiography.
This little cameo, revolves around a man who in his time, was both a "skimmer" and a "fish head".
Like many of you, I love to read about Royal Navy men [and perhaps one day we will read of Royal Navy women, but as yet, they haven't had time to establish themselves], and I like to read cameo's [or listen to a raconteur relating a good tale] especially about lower deckers, famous, infamous or otherwise.
Peter agreed to loan me his fathers papers to see if a cameo could be written, and what follows uses the papers and Peter's own recollection of his Dad.
Before I begin, let me tell you that I have become au fait at decyphering old naval Service Certificates.