Merlin Entertainments, who own the attraction, said it has received “a number of requests for the character to be renamed to Richard due to the apparent rude nature of his nickname”.
Dick Turpin was an infamous highwayman in the 1700s. He was executed in York in 1739 for horse theft.
In the new exhibition, guests will listen to scary tales while sat in a dark carriage.
The stories will reflect the hold-ups that highwaymen of the era made their trademark.
A view of the York Dungeon attraction sign in York.
Anna Gowthorpe
Turpin will order guests to “stand and deliver".
Despite excitement about the attraction, some parents have asked that the name be changed from Dick, to avoid children being exposed to a rude word.
The York Dungeon spokesman said: “We have had a few complaints about it, which is silly. His name is Dick Turpin.”
GB News presenter and MP for Shipley, Philip Davies, said: “I don’t know who the biggest morons are: the people who have complained or the people who might be thinking of doing something on the back of the complaints. It is a photo finish which is the most idiotic.
“It is the most ludicrous thing I have heard in my life. They should tell people who complain to get a life.
“Thank God the museum are saying they are not changing it.
"Let us hope this is the start of a fight back for common sense.”
The Telegraph reported Howard Johnson, a co-owner of the Eden Camp Modern History Museum, a rival Yorkshire attraction, saying: “A vote for common sense. Ignore these woke idiots.”
Mark Mattinson, general manager of The York Dungeon, said: “Our Dick’s Back carriage ride is the grand finale of our York Dungeon tour, and thousands of guests have already enjoyed this thrilling end to their visit.
“We were shocked to receive complaints asking to change his name but despite any potentially rude connotations, we’re here to say that Dick is here to stay.”