This article aims to studying how to solve dynamic Sylvester quaternion matrix equation (DSQME) using the neural dynamic method. In order to solve the DSQME, the complex representation method is first adopted to derive the equivalent dynamic Sylvester complex matrix equation (DSCME) from the DSQME. It is proven that the solution to the DSCME is the same as that of the DSQME in essence. Then, a state-of-the-art neural dynamic method is presented to generate a general dynamic-varying parameter zeroing neural network (DVPZNN) model with its global stability being guaranteed by the Lyapunov theory. Specifically, when the linear activation function is utilized in the DVPZNN model, the corresponding model [termed linear DVPZNN (LDVPZNN)] achieves finite-time convergence, and a time range is theoretically calculated. When the nonlinear power-sigmoid activation function is utilized in the DVPZNN model, the corresponding model [termed power-sigmoid DVPZNN (PSDVPZNN)] achieves the better convergence compared with the LDVPZNN model, which is proven in detail. Finally, three examples are presented to compare the solution performance of different neural models for the DSQME and the equivalent DSCME, and the results verify the correctness of the theories and the superiority of the proposed two DVPZNN models.