RC, it is referred to that way in the same way that we say Gregorian Chant or the Julian Calendar. It does not belong to Paul VI any more than Gregorian Chant belongs to Pope Gregory or the calendar to Pope Julius. These are the popes who promulgated them. There are many other promulgations that are called by the name of the person who authorized it.
Remember, we have a Dominican Rite, but it has nothing to do with St. Dominic. It developed within the Order of Preachers. We have Roman Breviary is called that because it was compiled in Rome, but it has its roots in Benedictine monasticism.
That which people call it is not relevant. Some people refer to the Roman Missal promulgated by John XXIII in 1963 as the TLM. It is not the Tridentine mass. It is a reform of the Tridentine mass promulgated by John XXIII. We read this in the motru proprio.
Also, I’m also 60 and have been a religious and a theologian for a long time and I can tell you that I have seen my fair share of OF masses on four continents. The abuses that I have seen are probably less than five times in my life time. Have I ever seen something out of the ordinary in an OF liturgy? Yes. Has it been catostrophic? No. The video that you posted is unfair, because it does not represent the majority of the celebrations of the mass in the Ordinary Form.
Many of the objections that posters have to the Ordinary Form are based on their experience, but also on their perception of what is good theology. This does not mean that they are good theologians. We cannot and should not underestimate the concerns of people. But we must not affirm those concerns at the expense of the universal Church. We must help people understand the difference between what they believe is good theology and what the Church teaches.
Most Catholics are not well versed in theology. Most do not have the proper background to interpret the documents of the Church. Most have the best intention in mind. We must respect their intention and desire to do the right thing. At the same time, help people understand what the Church teaches about liturgy and sacraments. It would be unfair to let people walk away believing that they have witnessed a catastrophic abuse, when they have not.
In closing, I’ll give an example. At the WYD mass in Sydney, I was there. I saw the seminarians do the liturgical dance with the Gospel book as they brought it up to the sanctuary for the readings. Some people questioned this as a liturgical abuse. This is not such an abuse. But those who don’t know what the reason was behind it, get confused and misunderstand.
Fraternally,
Br. JR, OSF