Magnetic nanoparticles (MNPs) have attracted a great interest in nanomedical research. MNPs exhibit many important properties, particularly, magnetic hyperthermia for selective killing of cancer cells is one of them. In hyperthermia treatment, MNPs act as nano-heaters when they are under the influence of an alternating magnetic field (AMF). In this work, micromagnetic simulations have been used to investigate the magnetization dynamics of a single-domain nanoparticle of magnetite in an external AMF. Special attention is paid to the circumstances dealing with a dynamic phase transition (DPT). Besides, we focus on the influence of the orientation of the magnetic easy-axis of the MNP on the dynamic magnetic properties. For amplitudes of the external AMF above certain critical value, the system is not able to follow the magnetic field and it is found in a dynamically ordered phase; whereas for larger amplitudes, the state corresponds to a dynamically disordered phase and the magnetization follows the external AMF. Our results suggest that the way how the order-disorder DPT takes place, and both the metastable lifetime as well as the specific loss power (SLP), are strongly dependent on the interplay between the orientation of the magnetic easy-axis and the amplitude of the external AMF.