Perhaps you have noticed that our full name is St John the Baptist Russian Orthodox Greek Catholic Church. To many people with knowledge of the history of the Church, especially history of Russian Church, this name might seem a bit confusing. Below is a decipher of our name.
"Russian Orthodox" We are Russian Orthodox by virtue of our main bishop (Patriarch Kirill) residing in Russia. In fact, the first Orthodox Christian bishop on North American soil was Russian. For awhile (until Russian Revolution), North America was under the jurisdiction of Russian Orthodox Church. Today, Russian Orthodox Church is one of the jurisdictions represented on our continent, among them are also Orthodox Church in America, Greek Orthodox Church, Antiochian Orthodox Church, Serbian Orthodox Church, and a few more. Even though we are under the jurisdiction of the Russian Orthodox Church, we are not restricted to ministering only to Russians or Russian decedents. We are part of the Universal Orthodox Christian Church, and therefore our doors are open to all who seek Christ.
"Greek Catholic" The original name of the parish in Russian is Русская Православная Греко-Кафолическая Церковь Св. Иоанна Крестителя. "Greek Catholic" in this case is not so much a translation, as more of a transliteration of "Греко-Кафолическая." "Греко/Greek" is a tribute to the fact that Slavic pagan tribes (who are the ancestors of most nations in the Eastern Europe) were enlightened, illumined, by the Gospel of Christ through the Greek missionaries in the 8-9th centuries. "Кафолическая/Catholic" means "wholeness," "fullness," "universal," as in Orthodox Church is whole, full, universal, cosmic, and all-embracing. Hence, "Greek Catholic" has nothing to do with Catholics or Roman Catholic church.
Some older Orthodox parishes in America, those at least 100 years or older, also have the "Russian Orthodox Greek Catholic" in their name. How did Orthodox parishes in the US come to have this name in the first place? Prior to the Bolshevik Revolution in Russia in 1917, Russian Orthodox Church did not have one fixed official name. Many names were used, among them: Orthodox Catholic Greco-Russian Church (Православная Кафолическая Греко-Российская Церковь), Russian Church (Российская Церковь & Русская Церковь), Russian Orthodox Church (Российская Православная Церковь), Russian Orthodox Catholic Church (Российская Православная кафолическая Церковь), Greco-Russian Church (Греко-Российская Церковь), Orthodox Greco-Russian Church (Православная Греко-Российская Церковь), Russian Eastern Orthodox Church (Российская Восточно-православная Церковь), etc.
In 1823, St Philaret, Metropolitan of Moscow published his famous catechesis with the following title: "Christian Catechesis of the Orthodox Catholic Eastern Greco-Russian Church" (a mouthful, yes). This goes to show that "Greek" and/or "Catholic" was used in the name of the Russian Church, but "Catholic" never referred to Roman Catholic church (because Russian Church is not part of it). A difficult word combination of "Greco-Russian" also points towards the canonical (official, legal) succession of Russian Church from the Byzantine (Greek) Church.
The name "Russian Orthodox Greek Catholic Church" was introduced for the Diocese of Russian Orthodox Church of Alaska and North America for the official use at the first All-American Council, which was held on February 20-22 1907 in Mayfield, PA, and was chaired by Bishop Tikhon (who later became Patriarch of Russia, died under Bolshevik yoke and was canonized a saint). The choice of this name was necessary for the official incorporation with the government, and important in the vision of St Tikhon for the future development of Orthodoxy in America. He intended to make comfortable the multitude of newly returned Uniates (also known as Greek Catholics or Byzantine Catholics, hence where the confusion about the name might stem from) into the True Faith and the Church of their ancestors.
St John the Baptist Church in Little Falls, being under the jurisdiction of Russian Orthodox Church from the parish's inception, received its full name by default, so to say. All the parishes under the same jurisdiction, that were formed after 1907, also received the same official name.