When building work was almost complete, the School Boards of Harthill Primary and Benhar Primary, wasted no time including the entire local communities in the decision making regarding the new school's name. Many suggestions were put forward and the School Boards put a short list of names to the public vote. Alexander Peden was the overwhelming winner with every single household in both Harthill and Eastfield using their vote, naming the school after the noted Covenanter, Alexander Peden. The school lies in close proximity to the Peden Stone which would have been used by Alexander and other preachers as a plinth.