Anglo-Saxon for "Royal Fortress," the name was given to a 7th century princess who founded an abbey, St. Kyneburgha. A church in England is named for her. This name is older than Kimberly, which means "Kyneburgha's Field." Kimber is the English spelling of Cymru (kimre) a Cornish word meaning Welsh.
Kymber (Is always spelled as Kymber, never Kimberley), originally used as an English surname, is both a male and female given name.