Considering the webpage you linked doesn't even call the station by its official name (in either language) as displayed on the front of the station and on the plaque near the entrance (it seems to think the station's official name is "VIA Rail Station"

), I would question the legitimacy of the "Canada's Historic Places" website.
Ottawa train station 2013 2
JustSomePics / CC BY-SA (https://creativecommons.org/licenses/by-sa/3.0)
View attachment 276603
Also, while it is true that both CN and CP used the station for about a decade (before VIA took over), that isn't enough to make its official name Union Station. While it was, at one point, a union station by definition, that doesn't make its name "Union Station." If it does, we should rename Montreal's train station to Union Station since it is used by Exo, VIA and Amtrak.

In fact, Ottawa's station is no longer a union station as VIA is the only railway to use it (Toronto's station is used by GO, VIA, and partially by Amtrak).
The reality is, I have lived in Ottawa for 30 years and you are the first person I have heard call it "Union Station." Renaming the O-Train station to Union would cause as much confusion, as renaming Bonaventure Station in Montreal to "Union." I still stand by my argument that the best new name for the O-Train station would be "Trembley - VIA Rail."