This was addressed in an interview with Discovery showrunner Aaron Harberts.
Q: Why is Michael Burnham’s name… Michael?
All right, so here we go. We've worked on a number of Bryan Fuller shows… Wonderfalls, Pushing Daisies. Many of his female protagonists have typically what you would call male names. Chuck was one. Jaye was another. When we all sat down, of course, the idea was going to be that she was going to have a male name, or typically male name. We were just pitching around the writers' room. We had a couple on the board and I said, "Well, how about Michael?" Because I had remembered a gossip columnist in Chicago. I used to work in Chicago in publicity, and Michael Sneed, she wrote for the Chicago Sun Times. Then, there was the bass player for The Bangles, a musician named Michael Steele. I'd always thought that the name Michael was just really cool and different. We pitched that to Bryan and he was like, "Let me think about that." That's how we seized on it, but I think it's a really cool name, and maybe we'll see some more women Michaels. Who knows?
INTERVIEW: Discovery Showrunner Aaron Harberts, Part 2
Obvious in-universe her father's name is Michael Burnham, so giving her a name after her father wouldn't be an especially odd thing to do, even if it's not the most usual name for a female child. You may note that other individuals have had traditionally female or male family names throughout history.