Kaj is a Swedish diminutive of Katherine. Katherine originates in Greek language and means "chaste, pure". It has been one of the most popular feminine given names over centuries and with various spellings all around the world. Historically, it was a favourite name especially in Christian world. Katherine is the name of many saints, the most popular probably being Catherine of Alexandria, a 4th century martyr. It was also a popular name within royalty in different countries. The variant spelling Catherine is also very frequent.