The star has previously discussed how his name became common among Caribbean families because of his forebear's role on the island.
Although there are no paper records to establish the link, it seems that New York's new chief of administrative services is among them.
Cumberbatch's performance in 12 Years A Slave, which has been nominated for several Academy Awards, including Best Picture, is not the first time that he has chosen a role that harks back to his family's ties to slavery. Abraham Cumberbatch, who was born in Bristol in 1726 and died in 1785, came from a family of merchants and adventurers and built the clan's fortune from a sugar plantation on Barbados.
The actor said that it was a "sort of apology" for this history when he played William Pitt the Younger, the abolitionist prime minister, in the 2006 film Amazing Grace about William Wilberforce's fight to eliminate the slave trade in the British Empire.
He once said that his mother, Wanda Ventham, the actress who also played his mother in Sherlock, encouraged him not to use his real name in his professional career because she was concerned that he could face claims for reparations from descendants of slaves.
The Cumberbatch family has faced no such lawsuits. But 14 Caribbean nations last year said they would seek reparations from the former colonial powers of Britain, France and the Netherlands for the slave trade. The countries have hired a firm of London lawyers that secured compensation from Britain for Kenyans who were tortured under British colonial rule in the 1950s.
The islands have said they will compile an "inventory" of damage suffered and demand an apology and financial damages. Britain abolished the slave trade in 1807.
Researchers said last year that an ancestor of Samantha Cameron, the Prime Minister's wife, received the equivalent of several million pounds in compensation when the British abolished the trade.
Benedict Cumberbatch
• Born in Kensington, raised in Chelsea and educated at Harrow.
• In 2012 he courted controversy by lamenting that he was a victim of "posh-bashing".
Stacey Cumberbatch
• Born in the New York borough of Queens, graduated as a lawyer and has spent a long career in city and state government.
• New York mayor Bill de Blasio said that her heritage "has driven her to excellence''.