"Rumi is our favorite poet, so it was for our daughter," he explained in an interview with Rap Radar hosts Elliott Wilson and Brian Miller, posted to his streaming service Tidal.
JAY Z, 47, is referring to Jalal ad-Din Muhammad Rumi, a 13th-century Persian poet. He remains a bestseller, especially in the U.S., according to the BBC, thanks to his poetry on love.
In regards to naming his son, Sir, JAY Z said the two agreed on the name after he was born.
"Sir was like, man, come out the gate. He carries himself like that. He just came out, like, Sir," the father of three said.
Rumi and Sir Carter, born in June, joined their big sister, 5-year-old Blue Ivy.
Speaking of their first born, JAY Z also explained during his Rap Radar interview how she came to freestyle on a bonus track on his latest album, "4:44."
The budding music titan freestyles a 45-second rap on a song aptly named, "Blue's Freestyle/We Family."
"She got the headphones and she climbed on the little stool, and then she just started rapping," JAY said. "I was like, 'Oh, s---.' I have [her full freestyle] on my phone."
JAY Z added that his daughter rapped for an impressive "five minutes!"
The bestselling rapper said he was most impressed by his daughter's hook in which she rapped: "Boom shakalaka/Boom shakalaka/Everything in shaka/ Everything in faka."
"She kept doing that 'boom shakalaka, boom shakalaka.' I was like, 'Oh, she understands the concept of a hook,'" he said. "She's 5, and she understands the concept of a hook. I was like, 'What the f--- is going on here?' One of the great memories."