The dynamic phase diagrams of a kinetic transverse Ising nanowire system are investigated in the presence of a time-varying (sinusoidal) magnetic field [ h(t) = h (0) sin(wt)] by using the effective-field theory based on Glauber-type stochastic dynamics. First, the time dependence of the magnetizations is studied in order to find the phases in the system. Then, the dynamic phase diagrams are presented in the (T, h), (T, r), and (T, Delta(S)) planes. It is found that the dynamic behavior of the system strongly depends on the values of the interaction parameters, and the different topological types of phase diagrams are obtained for the case of ferromagnetic and antiferromagnetic interactions. We observe the F, AF, and P fundamental phases and two mixed phases composed of binary combinations of the fundamental phases as well as a dynamic zero-temperature critical point and a multicritical point, depending on the interaction parameters. Moreover, the system also displays dynamic tricritical points, re-entrant behaviors as well as one and two compensation points.