With increasing importance of digitalization and requirements of data collection and mining in the mobility sector, the demand on privacy protection of mobility trajectories is also growing. Mobility trajectories offer important insights which could be applied for traffic simulations and planning. However, they also allow one to understand the behavior of individual users. These serve as potential vulnerable attack points, as the data may allow conclusions to be drawn about personal situations. Anonymization methods are therefore required for the use of these privacy-sensitive data. One of the central challenges is on the one hand to undermine the traceability to specific individuals and on the other hand to keep the overall usability of data as much as possible. This can be ensured by generation of anonymized synthetic data with a Local Differential Privacy mechanism and the use of publicly available geographical maps that display among others streets, railroad lines and pedestrian zones. In this paper, a map matching algorithm is applied to synthetic trajectories created with a Local Differential Privacy mechanism. This way, anonymization as well as a high level of utility for the synthetic mobility trajectories is achieved.