I found this:-
There are competing theories as to etymological origin of the word "Jack". John P Monro, Bowls Encyclopaedia (3rd ed), gives that the name 'jack' is derived from the Latin word jactus, meaning a cast or a throw. A sport played by young men called "casting the stone" is mentioned by William FitzStephen, a close friend of Thomas à Becket, in the preface of his biography Vita Sancti Thomae written during the twelfth century . Casting of stones translates in Latin as "jactu lapidum" and was a game in which rounded stones were thrown at or bowled towards a target object and so some are persuaded that the modern word 'Jack' derives originally from this term.
But the most straightforward theory and the one most favoured by this author is that it appears that Jack in some contexts meant a slightly smaller version of something. For example a jack-rabbit is a little rabbit. In this case a 'Jack-Bowl', was the little bowl, later shortened to 'Jack'. In 1697 R. Pierce wrote "He had not Strength to throw the Jack-Bowl half over the Green".