According to series creator Bryan Fuller
(who has a history of inventing female leads with male names for his various TV shows), Michael is named after her father Michael Burnham, while her mother's first name is Gabrielle. See more
Cmdr. Michael Burnham
[of her mother
She was right. What fight are we supposed to be continuing, Spock? Everything we try fails. Now, with no suit... no time crystal... it'll always be one step ahead of us.
Respectfully, Dr. Burnham was incorrect. Now does matter. What happened before no longer exists. What will happen next has not yet been written. We have only now. That is our greatest advantage. What we do now, here, in this moment, has the power to determine the future. Instinct and logic, together. ...