The name was chosen three years ago, but with the project now derailed and possibly taking a new direction, some are calling for a new name.
In a letter to the city council, Raleigh Police Detective Kevin Rooker says "there is tremendous opposition to naming this building after a politician."
And Rooker's Facebook site -- focused on getting the building renamed -- had more than 260 members as of Wednesday.
But local activist Octavia Rainey, who supports using Lightner's name, says she is shocked by the new debate.
"When we talk about safety, we talk about justice and justice for all and that's what Clarence Lightner stood for," she said.
Lightner's name was recommended by a committee, that was formed to figure out what to name in his honor, shortly after he died back in 2003. They considered streets and parks, but decided a building would be best and the safety center was available.
"The emphasis at that time was to find something to honor Clarence Lightner, that's how it was selected," Raleigh Mayor Charles Meeker said.
But Rooker says a public safety center should be named after someone in public safety.
In his letter he asks, "Why name it after a mayor that served for only two years and was not an advocate for the police or fire departments?"
Meeker countered that Lightner was more than just a just a mayor.
"He also was active in the civil rights movement on the non-violent side," Meeker said. "He helped keep peace here in 1968 when other cities had riots. So he was a big figure here and not just a politician."
And with the safety center now in danger of not being built at all, Rainey worries that a fight over its name will just complicate things further.
"All you're doing there is throwing something else onto the fire," she said.
ABC11 contacted Lightner's family for comment and his son Bruce said in a statement that they are shocked and saddened by Rooker's letter. They compared him to a "tea partier" saying, "let's just let Rooker be off his rocker."