That’s how I always heard it works as well. It’s more of a popular acclamation than an official Church designation. Of course, I don’t think that makes such a thing meaningless.
So far, the only two popes that are referred to as “the Great” are
Pope St. Leo the Great (440-461) and
Pope St. Gregory the Great (590-604). I’ve also sometimes seen
Pope St. Nicholas (858-867) referred to as “the Great”, but not as often. In any case, it’s been a while.
Personally, I have a great love and admiration for John Paul II. All any of us can do at the moment is guess as to how history will remember him. Whatever you say about his disciplinary action (or lack thereof), I believe he has a large body of great accomplishments that eclipses his shortcomings. He reigned for more years than all but 3 or 4 other popes, he revised Canon Law, put out a new universal Catechism, crafted the “Theology of the Body”, visited more countries than any previous pope, etc., etc. He didn’t do
everything, but he did a lot. I wouldn’t be surprised if the title sticks. But, again, none of us can really know for sure this side of heaven.