The name Trinham is one of many devolved from the name Trenholm(e), originally of York U.K. and more originally from the Scandinavian, probably migrating with the Viking conquests of the East English coast. Three Trenholm families migrated to Nova Scotia in the later 1700's. The Trenholm's in Nova Scotia, I have been told, sound their name 'Trenum'. If so this may account for the name ‘Trinham.’ John was not literate, and like many signed with an X mark. We know that he accounted for his parentage being Trenholm because he passed that information on to his grandson who recorded it in his own life’s story.
Back in Halifax in 1795, 'John Trenholm' joined the Royal Navy and being unable to write, gave his name as what sounded like 'John Trenum' to the clerk and it was entered into the ship's muster roll as John Trennan. At his marriage at Great Yarmouth his name was entered by the officiating cleric as John Trunham. A little later he went on to serve in the English army as John Trunham.
After discharge from the army, census records show the name as Trinham. 'John Trinham'. It seems that his wife, in his long absence overseas, may have been responsible for this variation and when John was discharged injured from army service he simply adopted this spelling of the name, possibly unaware or unconcerned at the change. This spelling for the name stuck, and has endured. From this beginning there has devolved two main families with this name. Both men were grandsons of this 'John Trenholm - Trinham', James Samuel Trinham who remained in England and his elder brother, John George Trinham who migrated to Australia. For the details, go to The Trinham Name
For an overview go to the Trinham Family Page This is Where to Start to Explore.