Transgender student advocate Jennifer Shields said students whose gender switch had been revealed against their will had their safety threatened on campus.
Outed students were subject to harassment and some had even stopped attending tutorials, putting studies in jeopardy.
"It's a very real stress," said Shields.
"The preferred name system at university is not entirely effective. One of my friends was too scared to go to class after she was outed."
The university said a number of students from the campus transgender community had already lodged an application.
Pro Vice-Chancellor of Equity Trudie McNaughton said the university agreed the inappropriate use of legal names could lead to "outing" and consequences to students' health, safety and wellbeing.
The only option was to legally change their name but cost was a barrier, she said. Research had highlighted significant disparities for transgender students and this was an immediate and practical step, McNaughton said.
According to a 2012 New Zealand Adolescent Health Survey, 1 per cent of students identified as transgender and a further 2.5 per cent were not sure of their gender.
This means as many as 400 students could be eligible for having all the costs associated with getting a new name reimbursed.
McNaughton said the university was also addressing the issue of gender-neutral bathrooms on campus after complaints transgender students were using the wrong toilets.
McNaughton said transgender students were entitled to use the toilet they preferred but the university would also make a point of clearly labelling existing unisex toilets.
Any future building projects would also include additional unisex toilets for the transgender community, she said.
