Plans to construct the building on the Barbadoes St site of the original Cathedral of the Blessed Sacrament were confirmed earlier this year, a change from earlier plans to build it on Armagh St.
The older cathedral opened in 1905 but was demolished in 2020 after irreparable damage in the 2010 and 2011 earthquakes.
The replacement will be called the Cathedral of the Blessed Sacrament - Te Hāhi Matua o te Hākarameta Tapu Rawa.
"In recent weeks, people's voices have been raised in support of this choice. They spoke of a long and treasured history of churches and the cathedral of the same name, in which they and their forebears received the sacraments, professed their love for a spouse and farewelled loved ones."
In a letter read at Masses this weekend, Bishop Gielen said the two-month journey to the announcement of the name was designed to help him "better understand the heart of the people".
The Blessed Sacrament signifies a central tenet of the Catholic faith - that Catholics receive the Body and Blood of Christ, in the form of bread and wine, at Mass.
Bishop Gielen said Catholics' affection for the name, which has been attached to multiple churches and a cathedral in Christchurch, was evident among the more than 2000 responses to a shortlist of possible names.
"Your heart, expressed through a desire for the name Blessed Sacrament, has won my heart," he wrote.
"Our path towards a new cathedral will take many years, but this is another important milestone on our way.
"As discussions loom about the design of our cathedral, that work will have the Blessed Sacrament - that source and summit of our faith - at its centre."
It will be the first new Catholic cathedral in New Zealand in 120 years.
