Forgive my bluntness, but absolutely not.
Today it's leetcode, yesterday it was hackerrank and tomorrow it might be who-knows-what. But what value does it add to know that by the tags? Are there leetcode experts with different experience than hackerrank experts?
Don't get me wrong: I'm in favour of questions stating where the problem came from. But that's already done and I don't see the added benefit of using tags for this. Keep in mind there's only room for 5 tags per question and enough questions are already at maximum usage.
Tags connect experts with questions they will be able to answer. But what is leetcode going to add that programming-challenge doesn't do already?
We used to do this. exercism for example, for questions from exercism.io. Do note that it's actually pointing towards programming-challenge now.