Natural human-robot interaction requires robots to link words to objects and actions through grounding. Although grounding has been investigated in previous studies, none of them considered grounding of synonyms. In this paper, we try to fill this gap by introducing a Bayesian learning model for grounding synonymous object and action names using crosssituational learning. Three different word representations are employed with the probabilistic model and evaluated according to their grounding performance. Words are grounded through geometric characteristics of objects and kinematic features of the robot joints during action execution. An interaction experiment between a human tutor and HSR robot is used to evaluate the proposed model. The results show that representing words by syntactic and/or semantic information achieves worse grounding results than representing them by unique numbers.