The dynamic magnetization of immobilized spherical single-domain magnetic nanoparticles (MNPs) with uniaxial or cubic magnetocrystalline anisotropy was studied computationally by executing simulations based on the Landau-Lifshitz-Gilbert (LLG) equation. For situations when a static magnetic field was suddenly applied and then removed, the effects of particle diameter and anisotropy (considering both type of symmetry and characteristic energy) on the characteristic magnetic relaxation time were studied parametrically. The results, for both anisotropy symmetries, show that when a static magnetic field is suddenly turned on or off the MNPs undergo a successive two-step or combined one-step relaxation. Whether a MNP relaxes with one or two steps when the field is turned on is determined by the competition between the energy of the applied magnetic field, the magnetic anisotropy energy, and thermal energy. When the applied magnetic field is suddenly turned off, our results show good agreement with theoretical predictions for the cases of [Formula: see text] and [Formula: see text], where [Formula: see text] represents the magnetic anisotropy energy barrier, [Formula: see text] is the Boltzmann constant and [Formula: see text] represents the absolute temperature. For the case of an applied alternating magnetic field (AMF) that is typical of magnetic particle imaging (MPI) applications, the effects of particle diameter and anisotropy symmetry were studied in terms of time-domain magnetization dynamics, dynamic hysteresis loops, harmonic spectra, and x-space point spread functions (PSFs). Results illustrate that the type of magnetocrystalline anisotropy (uniaxial versus cubic) has a significant effect on the MPI performance of the nanoparticles. These computational studies provide insight into the role of particle diameter and magnetic anisotropy on the performance of MNPs for applications in magnetorelaxometry and MPI.