The call from Christian Unkovich-McNab and Sam Murphy came after the Roman Catholic Bishop of Dunedin, the Most Rev Michael Dooley, said yesterday he was still to decide if the Dunedin college - named after former Bishop John Kavanagh - needed a new name.
He wanted more time to "thoroughly" review the issue, and in the meantime had called in the Catholic Church's National Office of Professional Standards to help.
"I hope that findings from such a review will help me to gain a better understanding of Bishop Kavanagh's involvement at that time," Bishop Dooley said, without giving a timeline.
The delay followed revelations by ODT Insight, which has since last July highlighted the extent of historic sexual abuse by priests, religious brothers and lay teachers within the diocese.
Much of it occurred under then-Bishop John Kavanagh, prompting calls from some survivors and advocates for the college's association with him to end.
That included the two former Kavanagh College pupils, who last year organised a public meeting and petition to press for change.
Mr Unkovich-McNab said yesterday they were "disappointed" to see the church "passing the buck" on the issue.
Bishop Kavanagh had either failed to act on past abuses, or been ignorant of them, and "either way he has completely failed to protect the most vulnerable people in the church community", Mr Unkovich-McNab said.
The views of survivors should be the focus, and the longer the name remained unchanged "the more harm occurs to people", he said.
"We are asking for Bishop Dooley to break the cycle and show compassion towards the many survivors of abuse within the Dunedin diocese during Kavanagh's time as bishop."
Bishop Dooley would not answer further questions, but acknowledged the process was taking time.
"This is a difficult process but I am determined to see it through as fairly as possible."
NOPS director Virginia Noonan confirmed her office would assist with the inquiry, but also declined to comment.
The delay was blasted by Dr Murray Heasley, a spokesman for the Network for Survivors of Abuse in Faith-based Institutions, who suggested NOPS' involvement was at the behest of the New Zealand Catholic Bishops Conference.
In doing so, they were "kicking the can down the road" with "predictable" results, he said.
"It can only be a total whitewash with survivor voices ignored yet again."
He called on Bishop Dooley to put an end to the link between the college and a period of "unspeakable horror" for survivors.
"Survivors and their families deserve not to have such a symbol enshrined on a building to remind them of the shocking abuse they suffered."
The call for a name change first emerged - and was rejected - in 2017, after Dr Heasley found a photograph of a former priest and paedophile, Magnus Murray, displayed at Kavanagh College.
Murray taught at St Paul's High School before it merged with other Catholic schools to create Kavanagh College, but it later emerged Bishop Kavanagh had moved him - first to Australia and later back to the North Island - when his offending was revealed in 1972.
Murray was not convicted until 2003, and not defrocked until earlier this year, placing Bishop Kavanagh's actions at the heart of the debate over the name change.
The call for a new name emerged again last year, following ODT Insight revelations, and was considered by the college board of trustees in November.
It was then referred to Bishop Dooley, who would only say he was "seriously" considering the issue.