We investigate noise effects in nanoscaled electrochemical sensors using a three-dimensional simulation based on random walks. The presented approach allows the prediction of time-dependent signals and noise characteristics for redox cycling devices of arbitrary geometry. We demonstrate that the simulation results closely match experimental data as well as theoretical expectations with regard to measured currents and noise power spectra. We further analyze the impact of the sensor design on characteristics of the noise power spectrum. Specific transitions between independent noise sources in the frequency domain are indicative of the sensor-reservoir coupling and can be used to identify stationary design features or time-dependent blocking mechanisms. We disclose the source code of our simulation. Since our approach is highly flexible with regard to the implemented boundary conditions, it opens up the possibility for integrating a variety of surface-specific molecular reactions in arbitrary electrochemical systems. Thus, it may become a useful tool for the investigation of a wide range of noise effects in nanoelectrochemical sensors.