No need to apologize for your likes or dislikes, but I don’t see how they are relevant here.
Even the definition for “a communion” that you posted says : “a religious group or denomination having a common body of beliefs, doctrines, and practices” (emphasis added) but you seem to entirely ignored the “or” and then run away with the “denomination” part of it. (Why post a quote if you’re then going to ignore what it says?

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This is an issue of semantics. I don’t believe the Catholic Church is “a religious group.” To me “a religious group” would be a religious community of some sort. The true Church is more than just a "religious group"
Also, you yourself recognize that Eastern Orthodoxy and Oriental Orthodoxy, which are not denominations, can each be called a communion, adding that “… there is primacy, but the entire communion isn’t under one hierarchy and under one Bishop like the Catholic Church”. Have you actually bought into the thinking of some Orthodox polemicists that Catholicism isn’t a communion but just an extension of the pope? May I say, yikes.
***I don’t agree with the Orthodox. I know how the relationship between the Eastern Churches and the Pope works.
I think it’s perfectly fine to “operate” our different Rites and Churches as a communion. Each Patriarch and Major Archbishop should be allowed to run his Church without interference from Rome (minus heresy or when asked to intervene). But there is a difference between operating as a communion and calling ourselves a Communion. ***
I assume you know what a false dichotomy is. Recognizing that Catholicism is a communion doesn’t mean that it isn’t the one true church.
***I can accept that the Catholic Church can be considered a “communion” and that operating the Eastern Churches (and any western churches that might return from Protestantism) as communions is a good idea. I read the document from the Vatican about it.
But I do not think it’s wise to make “Communion” part of our name. The Vatican’s document was worried about that too (Section II, part 8). Changing our name from the “Catholic Church” to the “Catholic Communion” or “Roman Communion” can have a negative reaction. It emphasizes that we have differences instead of emphasizing our similarities. No matter our Rite, the Pope is the single voice for the Catholic Church, the sole bishop protected by Christ from teaching error in Faith and Morals. We cannot have each patriarch trying (or perceived) to be publicly equal to the Pope (the Orthodox have this problem amoung themselves, let alone with the Pope).
The better thing to do is to emphasize that we are all the Catholic Church. Let’s stop focusing on our differences. Let’s focus on being Catholic.***
That’s just a few comments about your reasoning.** I won’t go on because I believe your misstatements mostly speak for themselves. ** ***This comment and some others are not very nice, and kind of snide. I’m debating your position. Not calling you dumb, being a jerk, etc.
I believe this is very nuanced. Look at the condition of the Anglican Communion. It’s falling apart. The Lutheran Communion is often splitting up, etc. Calling ourselves the Catholic Church has worked for 2000 years. I don’t think there is a reason to change our name from the “Catholic Church of Christ” to the “Catholic Communion of Christ” or the “Roman Communion of Christ.”***