Hello Stuart, I have been researching a set of Scots names, and one of them is Gattonsby. My own heritage follows from Scots Covenanters who managed to remain in Scotland in Ettrick Forest, emigrating from there in late 18th c. to New York. Another line of Hoys were transported earlier apparently to Massachusetts and Maine, New England, in 1650 and 1651. In this neighborhood at that time appeared a John Gattinsby,son-in-law to Thomas Spencer, having married Susanna Spencer--June 5, 1679 (York [Maine] Deeds, Book V, Part I, Folio 12.
My surmise, wild as it may seem, is that some of these Scots Covenanters were stubborn and rebellious enough to alter their names after capture and in prison. The name Gattisnby/Gattonsby then would signal "from or for the town by Gala [Water]" --that is, Gattonside [Gala-town-side], across the Tweed from Melrose. There was a fairly resilient set of independent types originating there who were stubbornly adhering to the Auld Kirk--Knox descendants, even (I'm related to them, of course!)
If you would like to chat further, let me know and we can exchange more information. Perhaps this interpretation may indicate why Gatensby/Gatenby family members would settle in Canada, and mix with Native American/First Nation/ Indigenous families (as I observe from a quick web search).