I also gave examples of other churches and communions that do not have the word "Christian" in their name, where there is no intent to "detach" themselves from Christ in their presentation of themselves to the world, as you wondered whether that was the intent of the Catholic Church in not using the word Christian in their official name.
While on the topic of the official name of the Church, I noted that "Roman Catholic Church" is not the proper name of the Catholic Church, which has several rites including the Roman one:
Although the Diocese of Rome is central to the Catholic Church, this does not mean that the Roman rite, or, as is sometimes said, the Latin rite, is co-terminus with the Church as a whole; that would mean neglecting the Byzantine, Chaldean, Maronite or other Oriental rites which are all very much part of the Catholic Church today, as in the past.
I most emphatically did not think that you had never heard of the Catholic Church or the Pope in Rome or the Roman Rite. Quite to the contrary, I would say that many if not most Catholics n the English Speaking world (where this term is quite common) are not aware that "Roman Catholic Church" is not the official name.
Since your question was sincere perhaps you could either disagree with some of the facts I posted in reply or ask for other ones to answer your question, or state it in the form of a proposition that we could discuss.