In the case of Holy Trinity, the patron chosen for the school are the Three Persons in One God, which is the Holy Trinity. The school's patronal feast day would probably be Trinity Sunday (which in many dioceses is the first Sunday after Pentecost, but I am not sure when it is in the dioceses of Australia).
The address for Trinity Grammar School in Victoria, Australia is 40 Charles St, Kew VIC 3101, Australia. Their phone number is 61 3 9854 3600 and they have 5 campuses.
Palmer Trinity School was created in 1991.
Trinity Law School was created in 1980.
Trinity Preparatory School was created in 1966.
Trinity School for Children was created in 1999.
Trinity Collegiate School was created in 1995.
Trinity College School was created in 1865.
Trinity-Pawling School was created in 1907.
Trinity Valley School was created in 1959.
Trinity School - Teignmouth - was created in 1979.
Trinity Anglican School was created in 1983.
Trinity School - Nottingham - was created in 1975.