Indeed, and we all confess that in the Nicene Creed. However, in antiquity the question would have been “What local church do you belong to?” and in sense it still is, because a series of schisms which I think all of us in Traditional Theology deeply regret hath resulted in various local churches no longer being in communion with each other.
Thus, the local churches under the patriarchate of Rome in Western Europe became the Roman Catholic Church, and subsequently, a major portion of the church in modern day Czechia and Slovakia became the nucleus of the Moravian Church, the churches of the various Electorates of Northern Germany and of the Scandinavian Kingdoms became the nucleus of the Lutheranism, the Church of England became the nucleus of Anglicanism, while Calvinism originated in Geneva and spread elsewhere in Switzerland, Germany, and especially the Netherlands and Scotland, where it formed the nucleus of the Reformed and Presbyterian denominations.
In the East, meanwhile, the local churches of Constantinople, Greece, Cyprus, Serbia, Bulgaria, Romania, Albania, Georgia, Russia, the Ukraine, Montenegro, Macedonia, Alaska and other lands became Eastern Orthodox. The Church of the East, headquartered in Seleucia-Cstesiphon, which a thousand years ago was the largest in size, both geographically and in terms of membership, remains the church of the Assyrians, who live predominantly in the Nineveh Plains, and in Kurdistan, East Syria and Iran, and represent the largest ethnoreligious group to speak Aramaic in the vernacular.
Also in Asia, Africa and the Caucasus Mountains we find the Oriental Orthodox, consisting of the Coptic, Armenian, Indian, Ethiopian, Eritrean and Syriac Orthodox, who together with the Eastern Orthodox share the responsibility for bearing the torch of Christianity in the face of unspeakable tortures, human rights abuses, terrorist attacks and other forms of persecution, since the rise of Islam, in Egypt, Syria, Lebanon, Turkey, Iraq, Iran, Armenia (which recently lost a portion of its territory to the anti-Armenian regime of Azerbaijan) and even in Ethiopia, which is home to the largest number (40 million), but which has a significant Islamic population, and the Ethiopian Christians were not spared martyrdom at the hands of ISIS, Kyrie eleison. These churches for the most part have a close working relationship with their Eastern Orthodox counterparts in Antioch, Alexandria, Jerusalem and Sinai.
In India, there has in the capital been increased persecution of Christians by Hindus including the brutal rape of elderly nuns; to my knowledge this has not yet spread to the Malabar Coast, which is home to the St. Thomas Christians*, or Nasranis, as they are referred to by Hindus as a caste (since Hindus must put everyone in a caste), but the Christians in India should remain in our prayers. In Pakistan, the mostly Anglican Christians have experienced extreme persecution in recent years, and persecution is heating up in the People’s Republic of China.
*The Nasranis take their name, St. Thomas Christians, from the fact they were evangelized by St. Thomas the Apostle prior to his martyrdom in 53 AD, when an enraged Hindu rajah threw a javelin at him; interestingly this makes them nor only the third largest religion in India, with only Hinduism and Islam having more members, but also one of the most long-present, being both older and existing in India for much longer than either the Sikhs or the Muslims, and there are two Christianw for every Sikh or Jainist (indeed Sikhism is only around 600 years old, and only about 270 years old in its present form).