Recently, 3D STEREO observations explained the 3D structure of EUV waves. Patsourakos and Vourlidas (Astrophys. J.700, L182, 2009), Veronig et al. (Astrophys. J.716, L57, 2010) and Selwa, Poedts, and DeVore (Astrophys. J.747, L21, 2012) reported on the dome-shaped EUV waves resulting from different events. Here, we model, by means of 3D MHD simulations, the formation of dome-shaped EUV waves in rotating active regions (ARs). The numerical simulations are initialized with idealized (multi-)dipolar coronal (low β) configurations. Next, we apply a sheared rotational motion to the central parts of all the positive and negative flux regions at the photospheric boundary. As a result, the flux tubes connecting the flux sources become twisted. We find that in all the studied configurations of idealized ARs, the rotating motion results in a dome-shaped structure originating from the AR. However, the shape of the dome depends on the initial configuration (topology of the AR). The initial stage of the wave evolution consists of multiple fronts that later merge together forming a single wave. The observed EUV wave propagates nearly isotropically on the disk and also in the upward direction. We remark that the initial stage of the evolution is determined by the driver and not caused by a magnetic reconnection event. At a later stage, however, the wave propagates freely. We study the different wave properties resulting from different driver speeds and find that independent of the initial AR topology the 3D dome-shaped wave is excited in the system. The symmetry of the 3D dome depends on the topology of the AR and on the duration of the driver. The EUV wave triggered is independent of the temporal profile of the driver. However, the properties of the wave (speed, sharpness of the cross-section, etc.) depend on the type of the trigger.