Why is the Catholic Church called "The Roman Catholic Church"?

Why Catholic Church is called “The Roman Catholic Church”?

The answer is simple:

The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with approximately 1.3 billion baptised Catholics worldwide as of 2017. As the world's oldest continuously functioning international institution, it has played a prominent role in the history and development of Western civilization. The church is headed by the Bishop of Rome, known as the pope. Its central administration, the Holy See, is in the Vatican City, an enclave within the city of Rome in Italy. - Catholic Church (Wikipedia)

The pope, living in Rome (Vatican) is head of the the entire Catholic Church, of both Catholics of Latin Rite and of all the Eastern Rite Catholics.

Of all the Cardinals of the Roman Catholic Church there are also cardinals of various Eastern Rites.

Confirming therefore the norm of the current Code of Canon Law (cf. Canon 349), which reflects the millennial practice of the Church, I once more affirm that the College of electors of the Supreme Pontiff is composed solely of the Cardinals of Holy Roman Church. In them one finds expressed in a remarkable synthesis the two aspects which characterize the figure and office of the Roman Pontiff: Roman, because identified with the Bishop of the Church in Rome and thus closely linked to the clergy of this City, represented by the Cardinals of the presbyteral and diaconal titles of Rome, and to the question Cardinal Bishops of the suburbicarian Sees; Pontiff of the universal Church, because called to represent visibly the unseen Pastor who leads his whole flock to the pastures of eternal life. The universality of the Church is clearly expressed in the very composition of the College of Cardinals, whose members come from every continent. - UNIVERSI DOMINICI GREGIS

What more needs to be said.

From the Catechism of Pope St. Pius X:

20. Q. And why is the true Church called Roman?
    A. The true Church is called Roman, because the four marks of Unity, Sanctity, Catholicity and Apostolicity are found in that Church alone which acknowledges as Head the Bishop of Rome, the Successor of St. Peter.

And The 1649 Douay Catechism:

174. Q. Why do we call the church the Roman Church?
     A. Because, since the transition of St. Peter's chair from Antioch to Rome, the particular Roman Church has been head of all the churches, and to her the primacy has been affixed.

There are two parts for this:

First part: The Catholic Church ('C' as capital) is that group of churches in communion with the pope. If a group isn’t in communion with the pope, it isn’t part of the Catholic Church.

Within the Catholic Church there are a number of individual churches, sometimes called rites. One of these is the Roman rite or Roman church. It includes most of the Catholics in the Western world. A Roman Catholic is a Catholic who is a member of the Roman rite.

There are many Catholics in the East who are not Roman Catholics, such as Maronite Catholics, Ukrainian Catholics, and Chaldean Catholics. These are all in communion with the pope, but they are not members of the Roman rite, so they are not Roman Catholics.

The Roman rite is not stricter than these other rights. They are equal. They all teach the same faith; it is only local customs that are different among them.

Second part: How the term Roman got attached to it?

It is not possible to give an exact year when the term "Roman Catholic Church," began to be called. The term is assumed to originated as a reference created by Anglicans who wished to refer to themselves as Catholic. They thus coined the term "Roman Catholic" to distinguish those in union with Rome from themselves.

From Catholic Answers:

Different variants of the reference "Roman" appeared at different times. The earliest form was the noun "Romanist" (one belonging to the Catholic Church), which appeared in England about 1515-1525. The next to develop was the adjective "Romish" (similar to something done or believed in the Catholic Church), which appeared around 1525-1535. Next came the noun "Roman Catholic" (one belonging to the Catholic Church), which was coined around 1595-1605. Shortly thereafter came the verb "to Romanize" (to make someone a Catholic or to become a Catholic), which appeared around 1600-10. Between 1665 and 1675 we got the noun "Romanism" (the system of Catholic beliefs and practices), and finally we got a latecomer term about 1815-1825, the noun "Roman Catholicism," a synonym for the earlier "Romanism."

The Catholic Church does indeed usually refer to itself just as "The Catholic Church". That is what it's Wikipedia article calls it (Wikipedia usually names all organizations according to what they call themselves). Many Catholic-related organizations just use the word "Catholic" in their names - CAFOD is an example; Catholic School boards are another.

The term 'Roman Catholic' was originally applied by people who disagree with the Catholic church's claim to be the church (when they were not just referring to it as 'the Roman Church'). Over the centuries the usage has mutated, and term has been applied for various reasons, and is used by many people as if it were the official name of the church. However the history of the usage is extremely complicated. Even the Catholic Church sometimes refers to itself as the "Roman Catholic Church", especially if there is any danger of confusion, or of offence. This Wikipedia article gives some history of the usage of the term Catholic.

Those of you with way too much time on your hands can go and look through the Wikipedia debates on the correct naming of the church in the Catholic Church talk pages.