Rome can claim ownership of the word, but that is mere semantics. For Rome is not holy, nor Catholic, nor in the real sense, the Church of Christ. In the false sense, they are a church, but they have long ago left being Christ's Church under authority of God. The name catholic in our day has digressed to denote a denomination rather than it's true meaning. But in the early Church, it was the title denoting it's universal nature, and had nothing to do with a denomination in Rome.
Denominations are an invention of man.
It's not a Roman Church, nor is it Baptist nor Presbyterian, but the one holy universal Church, which is beyond the bounds of denominationalism. In the big picture, nothing has really changed today. The one Holy Universal Church because it is fulfilling it's commission to go to the ends of the earth with the gospel. It exists all over the world and has gone by many denominational names. Every educated scholar of course knows this.