To quote from the Kipling Society's Notes to My Boy Jack referred to by DaveRo a few posts earlier:

The ‘Jack’/John confusion

The modern understanding of the poem has been bedevilled by the presumption that ‘Jack’ of the poem is to be equated with Kipling’s son John, an identification set in motion by David Haig in his playscript ‘My Boy Jack’, first published and performed in 1997.

This identification was reinforced in 1998 by Major and Mrs. Holt’s book entitled My Boy Jack? The Search for Kipling’s Only Son (latest edition 2007) and further reinforced by the television film "My Boy Jack". Derived from Haig’s play, it was first shown in the UK to an audience approaching six million on Remembrance Day 2007 and premiered in the United States in April 2008. For these viewers, the John=Jack equation is cemented in the closing shot where Haig, playing Kipling, reads the poem to himself. This equation, supported by the University of Sussex, was further endorsed by the Imperial War Museum in its "My Boy Jack" exhibition from November 2007 to February 2008. Yet, exactly as John signed his last letter home, written when he was close to the front line, a letter from the Sussex archive, prominent in the publicity for the exhibition, within the family John was John, never Jack, Jack being the name of the family dog.

Given the occasion of the poem, heading the reports on the Battle of Jutland with its great loss of life, ‘Jack’ is evidently the eponymous Jack Tar; and if one is seeking to attach the poem to any individual ‘Jack’, that would be young John Cornwell, the boy sailor (referred to in the press as ‘the Boy Jack’) whose bravery at the Battle of Jutland was recognised with the award of a posthumous Victoria Cross on 15 September 1916.

But even that identification was overridden by Kipling in the Inclusive Edition (1919) in which he added the years ‘1914-18’ below the title, so disengaging the poem from its original Jutland context, and its possible association with Jack Cornwell, and transforming it into an in memoriam tribute for all those who died at sea and conveying words of stern comfort for those who mourned them.

A judicious view of the John/Jack issue is taken by Andrew Lycett when he remarks that "My Boy Jack" reveals that Kipling ‘could call on a vast reservoir of pain at the loss of his son’ (p. 471), a comment that does not require us to make any identifications but points to the one of the poem’s most immediate emotional sources.