There is a certain amount of freedom within the various Christian Churches to employ or ascribe certain titles to particular saints or blessed in their own way (or traditions).
The title of Doctor of the Church was first instituted officially on September 20, 1295 by pope Boniface XIII, when he accorded this title to four saints, Pope Gregory the Great being the first.
"The Doctors of the Church are great saints known for their defense and explanation of the truths of the Catholic Faith. The original eight Doctors of the Church—four Western (Saint Ambrose, Saint Augustine, Pope Saint Gregory the Great, and Saint Jerome) and four Eastern (Saint Athanasius, Saint Basil the Great, St. Gregory Nazianzen, and St. John Chrysostom)—were named by acclamation, or common acknowledgment; the rest have been named by various popes, starting with the addition of St. Thomas Aquinas to the list by Pope Saint Pius V in 1568."
Even within the Catholic Church, various local churches and Rites have added their own saints to the official Catholic list of 34 Doctors of the Church. If this freedom exists in the Catholic Church, it follows then that other denominations have the same freedom!
"In addition, some parts of the Roman Catholic Church have recognized other individuals with this title. In Spain, Fulgentius of Ruspe and Leander of Seville have been recognized with this title. The Syro-Malabar Catholic Church has recognized Ambrose, Jerome, Gregory the Great, Augustine, Athanasius, Basil, Gregory of Nazianzus, and John Chrysostom, as well as Ephrem the Syrian, Isaac the Elder, Pope Leo I, John of Damascus, Cyril of Alexandria, Cyril of Jerusalem, Epiphanius of Salamis, and Gregory of Nyssa. The Chaldean Catholic Church has recognized Polycarp, Eustathius of Antioch, Meletius, Alexander of Jerusalem, Athanasius, Basil, Cyril of Alexandria, Gregory of Nazianzus, Gregory of Nyssa, John Chrysostom, Fravitta of Constantinople, Ephrem the Syrian, Jacob of Nisibis, James of Serug, Isaac of Armenia, Isaac of Nineve, and Maruthas."
As for the Eastern Orthodox Churches:
"The Eastern Orthodox Churches honors many of the pre-schismatic saints as well, but the application of the term Doctor or Father of the Church is somewhat more flexible than in the West, and it is misleading to look for lists of officially recognized Doctors. An Eastern Orthodox understanding of such pillars of the Church include saints such as Photios I of Constantinople, Gregory Palamas, Nicodemus the Hagiorite, and possibly even more recent saints such as Nektarios Kefalas. An exception to this flexibility is the grouping of Basil the Great, Gregory of Nazianzus, and John Chrysostom, universal teachers or Doctors who are collectively known as the "Three Hierarchs" and represent the Christianization of the Hellenic tradition and education."
The Eastern Orthodox uses various other titles that other denominations generally do not invoke for their saints. Their traditions remain quite valid.