Bishop Grosseteste University (BGU) will be called Lincoln Bishop University if the idea is approved by the Office for Students.
The university said the changes would "better represent" their location.
Bishop Conway said he was a "great devotee" of his predecessor Robert Grosseteste, the 13th Century scientist, philosopher and educator who the university is currently named after.
He told the BBC: "I do regret that this university sees this as a necessity when the title has been so dear to generations of students.
"There's a lot to be said for having a very clear identity and the university's choosing to alter that identity to a degree.
"The name is unique and it does say something about the association of education with the cathedral and with our history as the people of Lincolnshire."
BGU has seen other name changes since it was first established in 1862 as an Anglican teacher training college for women.
It changed its name in 1962 to honour the former Bishop of Lincoln, Robert Grosseteste, and was granted university status in 2012.
The news of the name change has been met with mixed reaction in the city.
Steve Rayment, 62, said: "Why is it going to change? It shouldn't be allowed. It's tradition and it's wrong. It's history".
70-year old Lynne Connelly told the BBC the proposal was a "pity" but Emily Hodson, 28, described the new name as "fine and catchy".
Officials at BGU said the move to Lincoln Bishop University would mark a "significant chapter" in a "journey of growth and development".