  We have studied the dynamical polarization and collective excitations in an
anisotropic two-dimensional system undergoing a quantum phase transition with
merging of two Dirac points. Analytical results for the one-loop polarization
function are obtained at the finite momentum, frequency, and chemical
potential. The evolution of the plasmon dispersion across the phase transition
is then analyzed within the random phase approximation. We derive analytically
the long-wavelength dispersion of the undamped anisotropic collective mode and
find that it evolves smoothly at the critical merging point. The effects of the
van Hove singularity on the plasmon excitations are explored in detail.
