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Security and especially privacy is an important requirement for the success of vehicular ad hoc networks (VANETs) in the future. To introduce and realize privacy a common method is to use pseudonyms to improve the unlinkability of nodes, events, and locations. Each node will own a multitude of pseudonyms and has to change them once in a while. The mobility of nodes has an important impact on the use and the change mechanism of pseudonyms in VANETs. This influence is analyzed by means of simulation and mathematical analysis. To have a simple yet solid mobility model the Manhatten grid mobility model was designed to model vehicle mobility. Using this model the two important parameters node re-interaction, how often and in what time intervals do nodes re-interact, and node quiet-time, how long should a node stay quiet before changing its pseudonym, are examined using simulation. In addition, an analytical method for determining the upper bound of the node quiet-time is presented. These results can mainly help to set parameters for pseudonym change protocols and estimate the impact of using these concepts in VANETs.