I get the association because of the new Boruto: Naruto Next Generation anime but i thought naruto-gaiden was for the stuff after the Naruto manga.
To answer the first question: yes, we do want a tag for it which is separate from Naruto. The chief reason is that these are different series; if you want prior examples, then one can look at the Dragonball collection of tags.
If we want to start thinking about the universe of Naruto, then we can talk about that bridge when we need to; I'm sure that there's already a convention for tagging questions in the same universe that we can adopt.
I would also argue against a synonym for naruto-gaiden. That's a mini-series unto itself, and while there may be significant overlap, I would imagine that questions related to the gaiden may not specifically be about the new series.
Yep. In fact, it's already created. The link below sends you to the Boruto tag section: