Probably named after Clara Holland, daughter of Joseph Holland of Holland House. Like Clara Park, Clara Road, Clara Way and the other streets named Clarawood, this street is located close to the former site of Holland House. According to Ros Davies, Joseph Holland was a stonemason, artist, antique dealer, landlord and landowner of 800 acres of East Belfast. He died in 1900 in Cherryville Cottage, Sandown Rd. Clara died aged 18 in 1899 and is buried in Belfast City Cemetery.
On the recommendation of the city surveyor, the committee approved of the proposal of the Housing Committee to name new streets on their property at Clara Park, As follows: Clarawood Crescent, Clarawood Park, Knockwood Crescent, Knockwood Park, Knockwood Grove, Knockwood Drive, Clarawood Grove, Clarawood Drive, Knock Grove, Knock Link. Knock Way, Knock Green. (Improvement Committee, 13th April 1954).