E! News reports that the couple named their newborns Rumi Carter and Sir Carter. The powerhouse duo's company filed trademark documents for the names on June 26, according to the United States Patent and Trademark Office.
They requested trademarks to be used for various merchandise, including baby teething rings, baby carriages and strollers.
The singer and the rapper welcomed their new daughter and son on Saturday, June 17. The twins join 5-year-old sister Blue Ivy, who arrived at the hospital with her dad shortly before her sibling's birth.
This news comes hours after Jay-Z dropped his latest album, 4:44, which reveals on the title track that his twins were conceived naturally.
"I apologize often womanize / Took for my child to be born / See through a woman's eyes / Took for these natural twins to believe in miracles / Took me too long for this song / I don't deserve you," he says.
The family of five is expected to remain at their newly rented, $400,000-a-month Malibu mansion for the remainder of the summer.
Photo Credit: Getty / Christopher Polk