According to the Daily Breeze, some City Council members want to name it after LAPD SWAT officer Randal Simmons, who died in a shootout earlier this year.
Simmons was an African-American, and the school is in a largely Latino community.
Some activists say it should be named after labor civil rights icon Cesar Chavez.
The school district will decide what the new high school will be named.
The issue may also play a role in the upcoming council election, as Julie Ruiz Raber, a Latina and former councilwoman is campaigning to get her seat back, the Daily Breeze reported, and has taken the lead in calling for the school-naming decision to be re-examined.
"If I had my choice, it would be Cesar Chavez," Raber told the newspaper. "That would be such an honor. He's the only Mexican-American hero for the Latino community."
City News Service contributed to this story.
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