Surface modifications of plasmonic nanoparticles with metal adsorbates are essential in applications such as plasmonic sensing, plasmon-enhanced photocatalysis, etc., where spectral broadening is usually observed. A single particle study is presented on plasmon damping by adsorption of platinum (Pt) clusters. Single particle dark-field spectroscopy is employed to measure exactly the same gold nanorod before and after the Pt adsorption. The Pt-induced plasmon damping in terms of linewidth increase is found dependent on the resonance wavelength of the measured nanorod, which is dispersive in nature. The measured dispersion generally matches the theoretical prediction, and it basically exhibits a gradual increase with decreasing resonance energy. This increase can be attributed to the fact that the nanorod as a better resonator is more susceptible to the Pt adsorption than the spherical particles. Moreover, simulated results based on discrete dipole approximation method further indicate that the damping is mainly contributed from the adsorbates on the ends of the nanorod and independent on the type of the metal adsorbed. Knowledge and insights gained in this study can be very important for the design and fabrication of plasmonic heterostructures as functional nanomaterials.