A hearing device, e.g. a hearing aid, is configured to be arranged at least partly on a user's head or at least partly implanted in a user's head. The hearing device comprises a) at least one input transducer for picking up an input sound signal from the environment and providing at least one electric input signal representing said input sound signal; b) a signal processor providing a processed signal based on one or more of said at least one electric input signals; c) an output unit for converting said processed signal or a signal originating therefrom to stimuli perceivable by said user as sound; d) a keyword spotting system comprising d1) a keyword detector configured to detect a limited number of predefined keywords or phrases or sounds in said at least one electric input signal or in a signal derived therefrom, and to provide a keyword indicator of whether or not, or with what probability, said keywords or phrases or sounds are detected, and d2) an own voice detector for providing an own voice indicator estimating whether or not, or with what probability, a given input sound signal originates from the voice of the user of the hearing device. The hearing device further comprises e) a controller configured to provide an own-voice-keyword indicator of whether or not or with what probability a given one of said keywords or phrases or sounds is currently detected and spoken by said user, said own-voice-keyword indicator being dependent on said keyword indicator and said own voice indicator.