Of the 22 Eastern Catholic Churches *sui juris *, 6 are Patriarchal (Melkites, Maronites, Chaldean, Syrians, Armenians, and Copts) and 4 are Major Archbishoprics. The remaining 12 are from Metropolitanates down.
The 4 MAs are the UGCC, the Syro-Malabar Catholic Church, the Romanian Byzantine Catholic Church, and the Syro-Malankara Catholic Church, the subject of the OP.
In the Catholic communion of churches and in the CCEO, the chief hierarch of each of the 4 Major Archbishoprics is officially known and titled “Major Archbishop,” although it is recognized that Major Archbishops function akin to Patriarchs.
However, the faithful of the UGCC feel that they should have the dignity of a Patriarchal Church, being the largest of the Eastern Cathoic Churches with about 6 million adherents. The Holy Synod of the UGCC thus declared their Church to be patriarchal and endowed their chief hierarch, Major Archbishop Lubomyr Husar (also a Cardinal), the title of Patriarch and submitted their decision to Rome requesting approval. The late Pope John Paul II did not act on their request and it remains unacted by Pope Benedict XVI.
Internally, Cardinal Husar is referred to as Patriarch by both the faithful and clergy. Officially and in communications with Rome, however, Cardinal Husar does not use the title “Patriarch.”
This state of affairs in the Syro-Malankara Catholic Church, with about 400,000 faithful, mimics that in the UGCC. Rome has not approved the use of the title “Catholicos” by the Major Archbishop of the Syro-Malankaras, although internally he is regarded as their “Catholicos.”