It is commonly accepted in the strong-laser physics community that the dynamical regime of atomic ionization is characterized by the Keldysh parameter γ . Two distinct cases, where γ < 1 and γ > 1, are associated with ionization mechanisms that are predominantly in the tunneling and in the multiphoton regimes, respectively. We perform fully three-dimensional quantum simulations for the ionization of the hydrogen atom by solving the time-dependent Schrödinger equation for a wide range of laser parameters encoded by the Keldysh parameter. We find that the meaning of the Keldysh parameter γ changes when the laser frequencyω is changed, and demonstrate that γ is useful in determining the dynamical ionization regime only when coupled with the scaled laser frequency when a large range of laser frequencies and peak intensities are considered. The scaled frequency relates the laser frequency ω to the classical Kepler frequency ωK of the bound electron. Together with the Keldysh parameter, the pair (γ, ) refers to a more realistic picture of the dynamical ionization regime. We refer to final momentum distributions of the ionized electrons at several interesting points on the (γ, ) landscape in order to infer whether the tunneling or the multiphoton mechanism is dominant in these regions.