The frequency-offset-governed range-angle-dependent dynamic beam pattern of frequency diverse array (FDA) constitutes a critical mechanism for enhancing spatial-domain covertness in wireless communication systems. This paper investigates FDA-assisted satellite covert communication. By considering covertness constraints based on average Kullback-Leibler (KL) divergence, frequency offset limitations, and power budget, we jointly optimize the satellite transmit power and FDA element frequency offsets to simultaneously maximize the time-varying covert rate and minimize the time-varying covert angle. To address practical channel dynamics, we develop a stochastic channel model incorporating Doppler compensation and channel aging effect mitigation for the FDA scheme. Closed-form and approximate expressions for the beam peak angle and half-power beamwidth (HPBW) with respect to frequency offsets are derived and analytically verified. The principle of linear uniform FDA frequency offset interval is established, with covertness quantified through KL divergence, enabling an optimized FDA frequency offset design from an angular perspective. To solve it, an improved deep reinforcement learning (DRL) with soft actor-critic (SAC) algorithm is proposed. Simulation results demonstrate that the interception probability is improved, and the proposed dynamic FDA algorithm exhibits better covert performance than other DRL-based methods.