Short nose or from the court
A modern phonetic spelling of the French surname Courtney. It likely originated as a nickname for someone with a short nose ('court nez') or as a locational name for someone living near a manorial court.
Less common today
Cortnee isn't in the latest US Top 1000. It last peaked at #2,732 in 1991.
US births per 5-year period, 1990βpresent (SSA data).