This paper presents two novel models, designated as efficient prescribed-time and robust zeroing neural network (EPTR-ZNN), which employ a novel activation function (AF) and adaptive dynamic parameter (ADP) to address the time-variant plural Stein matrix equation (TV-PSME). The EPTR-ZNN model is proposed by combining the novel AF with the standardized ZNN design process. In comparison to traditional fixed parameter (FP) ZNN models, the EPTR-ZNN model exhibits a faster convergence rate, enhanced computational efficiency, and stronger robustness. To further improve these performance characteristics, we replaced the FP in EPTR-ZNN model with an ADP to develop the EPTR-DPZNN model. In contrast to traditional divergent dynamic parameters (DPs), the ADP can be adjusted in a synchronous manner as the model converges, thereby enhancing the computational efficiency. Theoretical analysis verifies the prescribed-time convergence and robustness of the EPTR-ZNN and EPTR-DPZNN models. Finally, simulation experiments demonstrate that the EPTR-ZNN model exhibits accelerated convergence compared to other ZNN models, while the EPTR-DPZNN model exhibits the best convergence performance, higher computational efficiency, and stronger robustness to time-variant bounded noise (TV-BN) and time-variant unbounded noise (TV-UN).