'Konny' is a feminine given name, or a diminutive hypocoristic Konstanze, which is less frequent than Constance, for which "Connie" is used more. There is an etymology that supposes an origin in the Latin cornu, us ("horn") or perhaps cornus, i ("dogwood" ornamental shrub), although the suffix -y is more English than Latin; and with that criterion it could even be by a diminutive of Kon, the Inca god of rain and south wind.
