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We study the dynamical polarization function and plasmon modes for spin-orbit coupled noncentrosymmetric metals (NCMs). These systems have different Fermi surface topology for Fermi energies above and below the spin degenerate point which is also known as the band touching point (BTP). We calculate the exact dynamical polarization function numerically and also provide its analytical expression in the long wavelength limit. We obtain the plasmon dispersion within the framework of random phase approximation. In NCMs, there is a finite energy gap in between intra and interband particle hole continuum (PHC) for vanishing excitation wavevector. In the long wavelength limit, the width of interband PHC behaves differently for Fermi energies below and above the BTP as a clear signature of the Fermi surface topology change. We find a single undamped optical plasmon mode lying in between the intra and interband PHC for Fermi energies above and below the BTP. The plasmon mode below the BTP has smaller velocity than that of above the BTP. It is interesting to find that as we tune the Fermi energy around the BTP, the plasmon mode becomes damped within a range of e-e interaction strength. For Fermi energies above and below the BTP, we also obtain an approximate analytical result of plasma frequency and plasmon dispersion which match well with their numerical counterparts in the long wavelength limit. The plasmon dispersion is $\propto q^2$ with $q$ being the wave vector for plasmon excitation in the long wavelength limit. We find that varying the carrier density with fixed e-e interaction strength or vice versa does not change the number of undamped plasmon mode, although damped plasmon modes can be more in number for some values of these parameters. We demonstrate our results by calculating the loss function and optical conductivity which can be measured in experiments.