If the any church calls a Council an Ecumenical Council, then the tag should be ecumenical-council, more tags are better, we don't have a problem on this site with too many tags being applied to questions. If only the Catholic Church recognizes it as such, the tag catholicism should be applied as well.
So, if there's questions about Vatican II we don't eschew the nomenclature that Catholics actually use in favor of nomenclature they don't use. A Church Council might be a Eucharistic Congress or a World Youth Day or a Big Honking Meeting of Methodists. As an example, we don't segregate biblical-basis from catholic-biblical-basis just because questions about Catholicism accept answers from Sirach and we don't separate orthodox-priesthood from catholic-priesthood just because Catholics and Orthodox have different ideas about priests.
as far as Vatican II goes, it's an Ecumenical Council to Catholics. It might more properly be called the first ecumenical council, but I digress. Here's how the wikipedia entry phrases it at least:
The Second Ecumenical Council of the Vatican, commonly known as the Second Vatican Council or Vatican II, addressed relations between the Catholic Church and the modern world. The Council, through the Holy See, was formally opened under the pontificate of Pope John XXIII on 11 October 1962 and was closed under Pope Paul VI on the Solemnity of the Immaculate Conception on 8 December 1965.
The Tag wiki should be edited to say explicitly that it refers to Church councils which are referred to by their respective denominations as Ecumenical Councils
If a question is asking for a Catholic interpretation of an event at the first 7 ecumenical councils, then you should use catholicism as well. But for the purposes of this site, we probably can treat the first 7 as historical record common of enough of Christianity in general that we don't need additional scoping (however it would be NAA to get an answer denying the council came in - or from a group that was specifically anathematized at that council).