Stacey Cumberbatch, New York’s new commissioner of citywide administrative services, is great at untangling bureaucratic knots and a proud granddaughter of Caribbean immigrants, Mayor Bill de Blasio said in naming her to the job on Friday.

He said nothing about her surname, however — a striking one, if a bit, well, cumbersome.

And one that she shares with a certain gangly but handsome British actor — best known as the eponymous detective in the BBC drama “Sherlock.”

Indeed, she and the actor Benedict Cumberbatch are related, if not by blood, then by geography and the complicated history of the slave trade, Ms. Cumberbatch said in an interview after she was introduced at City Hall.

Image Benedict Cumberbatch, star of BBC drama "Sherlock," shares a history with Stacey Cumberbatch. Credit... Gabriel Olsen/Getty Images

Ms. Cumberbatch said her ancestors were slaves in Barbados. The British Mr. Cumberbatch’s fifth great-grandfather, she said, owned a plantation in Barbados. It was common for slaves in that era to take the surname of their owners.