Mg ii h and k and Hα spectra in a dynamical prominence have been obtained along the slit of the Interface Region Imaging Spectrograph (IRIS) and with the Meudon Multi-channel Subtractive Double Pass spectrograph on 2013 September 24, respectively. Single Mg ii line profiles are not much reversed, while at some positions along the IRIS slit the profiles show several discrete peaks that are Doppler-shifted. The intensity of these peaks is generally decreasing with their increasing Doppler shift. We interpret this unusual behavior as being due to the Doppler dimming effect. We discuss the possibility to interpret the unreversed single profiles by using a two-dimensional (2D) model of the entire prominence body with specific radiative boundary conditions. We have performed new 2D isothermal-isobaric modeling of both Hα and Mg ii lines and show the ability of such models to account for the line profile variations as observed. However, the Mg ii line-center intensities require the model with a temperature increase toward the prominence boundary. We show that even simple one-dimensional (1D) models with a prominence-to-corona transition region (PCTR) fit the observed Mg ii and Hα lines quite well, while the isothermal-isobaric models (1D or 2D) are inconsistent with simultaneous observations in the Mg ii h and k and Hα lines, meaning that the Hα line provides a strong additional constraint on the modeling. IRIS far-UV detection of the C ii lines in this prominence seems to provide a direct constraint on the PCTR part of the model.