Ontario, the province, may not have existed by that name in 1865 but the lake did. Perhaps the names of the other lakes were not as suitable. Also, conferences concerning Confederation were in progress at the time and the name may already have been suggested. Certainly Tilley supported confederacy and so did Albert James Smith. That support was not universal.
The Maritime provinces initially planned to amalgamate separately from Upper and Lower Canada which were also talking about forming a nation in response to a perceived threat. The Canada's recognized the impracticality of joining without the connection to the Atlantic and went to enormous lengths (mostly involving money and liquor, a staple of NB elections) to convince the Maritimers to join in. The matter was hotly contested with New Brunswick the decider as it was split so evenly.
It is possibly then that about 1864-1867, Sir John A. (later Prime Minister) may have been actively working in New Brunswick to achieve his goals. Moncton, not only as a population centre, but as a communications centre (until at least the 1980's) and also a central location in the bilingual division of the province, would have merited his attention. He seems familiar with the area and mentions Moncton, Salisbury, Harvey, etc. in Commons Debates of 1889; referring to his favourite issue, railways.
I cannot find any mention of his having been in Moncton. Even the more famous visit to Charlottetown was by ship by way of the St. Lawrence. Nevertheless he knew of the place.
I believe the Elliott's you mention were connected to the Steeves'. William Henry Steeves from Hillsborough was also a Father of Confederation although not, it appears, a leader of a government.