I had a brief discussion about this (naming conventions for international teams) with BigEd I believe a few weeks ago. As stated here the rule is to use the country and I believe have different TIDs for each country relating to different sports.
I think there is a discussion to be had around making some of this country naming clearer as it is easy to link to the wrong TID and almost all these international teams to have a nickname/moniker of varying degrees of officialness (so to speak).
Just for New Zealand teams for example (some of these are a bit silly and I have no idea why the women's teams almost all get Ferns):
Men's rugby: All Blacks
Women's rugby: Black Ferns
Men's cricket: Black Caps
Women's cricket: White Ferns
Men's football/soccer: All Whites
Women's football/soccer: Football Ferns
Men's rugby league: The Kiwis
Women's rugby league: Kiwi Ferns
Women's netball: Silver Ferns
Men's softball: Black Sox
Women's softball: White Sox
Men's baseball: Diamondblacks
Men's basketball: Tall Blacks
Women's Basketball: Tall Ferns
Men's and women's bowls: Black Jacks
Men's and women's hockey: Black Sticks
Men's ice hockey: Ice Blacks
And a personal favourite... Men's badminton: Black Cocks (I don't know if this is still a thing in this PC world but it once was!)
These were just off the top of my head and I am sure there are dozens more.
Perhaps it is worth discussing whether it is easier to have some differentiation than potentially end up with dozens of TIDs that state "New Zealand".
Also if there are any rugby card questions feel free to contact me. I know a reasonable amount about the sport and a little about the history of cards, at least in NZ. There is another member here much more knowledgeable than myself but their username eludes me currently.