Observations of sungrazing comets can be used to probe the solar corona, to study the composition of the comets, and to investigate the plasma processes that govern the interaction between the coronal plasma and cometary gas. UVCS observations of the intensities and line profiles of H I Lyα trace the density, temperature, and outflow speed of the corona. Analysis of H I Lyα observations of comet C/2002 S2 showed a surprising split in the comet's Lyα tail and an asymmetry of redshifted and blueshifted emission across the tail axis. It was suggested that the velocity structure might result from a population of neutrals produced by charge transfer between pickup ions and cometary neutrals. Here we present numerical simulations of the H I Lyα intensity and velocity centroid for sungrazing comets under the assumptions that the magnetic field and solar wind are radial. The models qualitatively reproduce the observations of Comet C/2002 S2 and potentially explain the split tail morphology that was seen in C/2002 S2 and also C/2001 C2. They also match the observed red- and blueshifts, though the solar wind velocity needed to explain the blueshift implies strong Doppler dimming and requires a higher outgassing rate to match the light curve. However, the models do not match the observations in detail, and we discuss the remaining discrepancies and the uncertainties in the model. We briefly discuss the implications for other UVCS comet observations and sungrazing comet observations with the Metis coronagraph.