In order to design magnetic nanoparticles that are optimized for biomedical applications such as hyperthermia treatment and magnetic particle imaging, their magnetization dynamics should be analyzed. Through conventional analytical methods related to magnetization dynamics such as susceptibility and the magnetization curve, the net properties of magnetization have been previously evaluated. However, an examination of net properties does not yield information related to the stochastic dynamics due to thermal fluctuations and systematic dynamics influenced by the anisotropy with respect to single particles. In this study, the time evolution of the magnetization and easy axis of an individual magnetic nanoparticle was numerically simulated using the Landau-Lifshiz-Gilbert equation in terms of magnetic nanoparticles with fixed and rotatable easy axes, solids and liquids, respectively. The superparamagnetic and ferromagnetic regimes of the Langevin dynamics were clearly discerned through evaluation of the effects of anisotropy and thermal fluctuation, and an index for determining the transition point between these regimes provided. In particular, effects related to the core volume and the anisotropy constant associated with the anisotropy energy were assessed using the Stoner-Wohlfarth model.