Covert communications hide the transmission of a message from a watchful adversary while ensuring a certain decoding performance at the receiver. In this paper, a wireless communication system under fading channels is considered where covertness is achieved by using a full-duplex receiver. More precisely, the receiver of covert information generates artificial noise with a varying power causing uncertainty at the adversary, Willie, regarding the statistics of the received signals. Given that Willie's optimal detector is a threshold test on the received power, we derive a closed-form expression for the optimal detection performance of Willie averaged over the fading channel realizations. Furthermore, we provide guidelines for the optimal choice of artificial noise power range, and the optimal transmission probability of covert information to maximize the detection errors at Willie. Our analysis shows that the transmission of artificial noise, although causing self-interference, provides the opportunity of achieving covertness but its transmit power levels need to be managed carefully. We also demonstrate that the prior transmission probability of 0.5 is not always the best choice for achieving the maximum possible covertness when the covert transmission probability and artificial noise power can be jointly optimized.