Court documents reportedly show the Tesla boss and Shivon Zilis filed a petition to change the name of the twins in April, to “have their father’s last name” and contain their mother’s last name as part of their middle names.
The children were born in November 2021, Business Insider reports.
A month later, a Texas judge approved the petition, the report added.
A court summary on the Westlaw legal research service showed a judge signed an "Order Changing the Names Of Multiple Children" on May 11 after the name change petition from the SpaceX owner and Ms Zilis made on April 25 this year.
The report said, without citing any source, that Ms Zillis has recently been floated as one of the people Musk could tap to run Twitter Inc after his $44 billion (£36) deal acquisition.
Ms Zilis, 36, is identified on her LinkedIn profile as director of operations and special projects at Neuralink, which is co-founded and chaired by Mr Musk, 51.
She started working at the company in May 2017, the same month she was named a project director in artificial intelligence at Tesla, where she worked until 2019.
She also serves as a board member at artificial-intelligence research firm OpenAI, which was co-founded by Mr Musk, according to her profile on LinkedIn.
The news of the twins’ arrival brings the billionaire’s total count of children to nine, Reuters reports.
He shares two children with Canadian singer Grimes, and another five kids with his ex-wife Canadian author Justine Wilson.
Mr Musk and Grimes welcomed their second child via surrogate in December.
Mr Musk and Ms Zilis did not immediately respond to Reuters’ request for comments.