Reconfigurable intelligent surfaces have emerged as a cutting-edge technology for next-generation wireless communications that are capable of reconfiguring the wireless environment using a large number of cost-effective reflecting elements. However, a significant body of prior studies has focused on single-layer surfaces that lack the capability of significantly mitigating inter-user interference. Moreover, previous studies mostly consider far-field operation and neglect working in the near-field region. In this paper, we propose a stacked intelligent metasurfaces (SIM)-assisted near-field multi-user multiple-input-single-output covert communication system. More specifically, we have a multi-antenna base station that is assisted with a SIM to serve multiple single-antenna users in the presence of multiple single-antenna wardens. We aim at optimizing the beamfocusing vectors at the BS and SIM phase shift matrices to maximize the sum covert rate under maximum transmit power budget constraint, quality-of-service (QoS) constraint for all users, and covertness constraint. Since the formulated problem is highly non-convex due to the coupling between the variables, we adopt alternating optimization to tackle it, where we divide the problem into beamfocusing sub-problem and SIM phase shift sub-problem, which are solved alternately until convergence. We leverage successive convex approximation (SCA) to solve the two sub-problems. Additionally, we formulate the SIM phase shift sub-problem using the widely adopted projected gradient ascent (PGA) method for comparison purposes. The conducted simulations reveal that the SCA-based algorithm outperforms the existing PGA-based algorithm as well as other benchmarks in terms of the achieved sum covert rate, demonstrating its consistent performance and robustness under various system parameter configurations.