The use of directional transmission in millimeter-Wave (mmWave) frequencies results in limited channel coherence time. In this paper, we take the limited channel coherence time into account for non-orthogonal multiple access (NOMA) in mmWave hybrid beamforming systems. Due to the limited coherence time, the beamwidth of the hybrid beamformer affects the beam-training time, which in turn directly impacts the data transmission rate. To investigate this trade-off, we utilize a combined beam-training algorithm. Then, we formulate a sum-rate expression which considers the channel coherence time and beam-training time as well as users' power and other system parameters. Further, a joint power and beamwidth optimization problem is solved by iterating between the power allocation and the beamwidth optimization. When allocating the power, we use the log-exponential reformulation and the sequential parametric convex approximation (SPCA) methods to solve the non-convex problem. Since beamwidth optimization involves too many variables, we propose an algorithm which iterates between clusters of users. Numerical results show that the optimized mmWave hybrid beamforming-NOMA system can achieve much higher sum-rates compared to NOMA with analog beamforming and traditional multiple access techniques.