From Chlorine Villa, the name of the residence of James W. Crawford, chemical and starch manufacturer (Belfast Street Directory 1880), but apparently with a re-interpretation as if it were an Irish place-name.
Change of street name, Chlorine Park to Cloreen Park. "Resolved: That the request of Mr. R. J. Nelson, owner of the new street for which the name Chlorine Park had been approved, to have the name changed to Cloreen Park be acceded to". (10th January 1939)