I wouldn't stay awake at night imagining that this is another great Roman plot. The word Catholic is not a trademark nor a proprietary term.
For example, in one of the myriad of church property rights cases between factions of Greek Catholic congregations in Pennsylvania during the mid-20th century, the Commonwealth Supreme Court rejected the claim by the Greek Catholic Bishop of Pittsburgh that the term 'Greek Catholic' was entitled to proprietary protection. That was one of the reasons why Rome changed the legal name of the (Ruthenian) Greek Catholic Eparchy of the United States to the Byzantine Catholic Church. In Canada they are known as the Slovak Greek Catholics and in Europe, just plain Greek Catholics. To clarify the property status of their congregations, they legally reincorporated local parishes as Byzantine Catholic so as not to leave open the door to future litigation by would-be Orthodox factions. FYI, the problem did not occur within the Ukrainian Greek Catholic community as the use of the nationality - Ukrainian - historically preceeded Greek Catholic, hence there was no confusion.
For that reason, you will still find some Orthodox parishes with the term 'Greek Catholic' within their legal names, such as "Russian Orthodox Greek Catholic', "Carpatho-Russian Orthodox Greek Catholic" and in a few instances, even plain old "Greek Catholic." Just remember, as Will Shakespeare observed, 'A rose by any other name would smell as sweet.'