(From Ancestry.com):
Cyr
French: from the Latin personal name Quiricus or Cyricus, Greek Kyrikos or Kyriakos, ultimately from Greek kyrios ‘lord’, ‘master’. This name was borne by a 4th-century martyr, a small child martyred with his mother St. Julitta in 304 ad (see Quilici). In North America it is sometimes Americanized as Sears.
Quilici
Italian: patronymic from the personal name Quilico, an altered form of Quirico, borne by a (probably fictitious) 4th-century infant saint, said to have been martyred at Tarsus with his mother Julitta, who was honored in the Middle Ages as a patron of children. The name is probably a blend of two other names, both borne by numerous early saints: Latin Quirinus (originally a title borne by Romulus, founding father of Rome, referring to the Sabine city of Cures) and Greek Kyriakos (a derivative of kyrios ‘lord’, ‘master’).