The 26,000-a-year school, in Hammersmith, will replace the role with “head of school” in order to make it more inclusive.
According to The Times, the change will take effect from the next academic year.
However the move has sparked backlash from some staff members, who claim it sends the message “that girls now have to be ashamed to be seen as girls”.
One source said: “Why do the girls have to change their name?
“They should be teaching young women to be proud of their sex, not ashamed of it. It’s very contradictory.
“How can you be a single-sex school that exists to empower girls to do well and at the same time support girls to identify out of being a girl?
“The school is trying to do the right thing but the problem is they are being badly advised. Why would parents want to send their daughters to a school where girls are not happy to be girls?”
Staff at the school were also told there were at least “150” gender identities at a webinar entitled Beyond the Binary: Understanding How to be Inclusive for All Gender Identities.
Around seven of the school’s 778 pupils identify at non-binary, which means they don’t feel comfortable being referred to as male or female.
The school said the main reason for changing the title of head girl was because many senior pupils feel they are young women, but admitted the “binary connotations” were a factor in the decision.
Sarah Fletcher, the school’s high mistress, said in a statement the school “would never encourage a student to ‘be’ anything in relation to their identity”.
“We want our students to be happy as themselves,” she said.
“Our focus is on providing a respectful, kind, safe and non-judgemental environment in which our students are free to explore their own identity.
“Young people are talking about gender identity and our role as a school is to equip the staff with an understanding that supports students’ ability to reach to them for support and navigate this safely.”
A spokesperson for the school told the Standard: “It was the suggestion of our senior students that we change the name from ‘Head Girl’ to ‘Head of School’ as more modern, age appropriate and inclusive. In doing so, we are returning to our roots.
“From our very foundation in 1904 and for decades afterwards, the senior student was called ‘Head of the School’, so in making the change, we are confirming, not denying, our ethos and traditions.”