The Fancy singer was the first musician featured in a new Vevo series, A.K.A., in which artists explain the origins of their stage names.
Azalea, whose birth name is Amethyst Amelia Kelly, explained there are two stories to why she chose her name.
She chose Iggy after a dog she had growing up, which was named after rocker Iggy Pop.
"One time he got bitten by a snake," she said. "And he couldn't move his legs, and I realized he had killed the snake."
The dog survived after three weeks at a pet hospital.
"I got a name-plate necklace made in his honor," Azalea added. "Everybody started to think that my name was Iggy so it kind of became my nickname and I took it on board and started rapping with it."
At first she just went by Iggy, but upon advice from her grandfather, she took on a surname as well.
"(He) said to me, 'You can't have a one-word stage name,' " she said.
She chose Azalea after the name of the street her family lives on.
"It sounds very feminine and I thought it would balance out Iggy being so masculine," the rapper said.
Azalea said she has no plans to return to her birth name.
"So if you see me on the street call me Iggy or I will kill you, seriously," she said laughing. "I really will."
Just how serious is that threat? Check it out below: