The actress revealed that she loves her character's name.
"I love all of it," she said. "I love having a male name. I think that it speaks to the gender fluidity of our future. ... I have been named after my biological father, so that's a sort of nod to the father-daughter dynamic on the show."
First Officer Michael Burnham is named after her biological father, Michael Burnham, but is raised by Spock's father, Sarek.
Martin-Green acknowledged that it's never been mentioned that Spock had a "sister" in previous iterations of the show, but she said, "We're working on it. Be patient with us." Burnham is the first human to attend the Vulcan Science Academy.
The actress said, "I am genuinely impressed with how they've woven me in." She added that she wants "Discovery" to resonate with lifelong Trekkies.
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"'Star Trek' has been around for a really long time. It's been a big part of people's lives and people's hearts for a long time," said Burnham. "I hope that we are showcasing why, with our iteration, it has been such a big part of our lives for so long."
Watch more of the interview above.