I find this extremely funny. Has this happened to other companies or just to Target?
Trademarks are per-country thing. They protect you from other companies in your country using the same name or branding (logos, slogans etc).
If you want to start operating in another country, you'd have to get your name/branding trademarked there. If there's already another company with that name, you then have to either try to negotiate licensing the name from them, or have to pick another name for that country.
Burger King in Australia is called
Hungry Jacks, because when the US chain started operating in Australia there was already one burger place in Adelaide that had that name. The owner wouldn't licence/sell the name to the US giant.