Phononics in two-dimensional (2D) materials is an emergent field with a high potential impact from the basic as well as applied research points of view. Thus it is crucial to provide strategies to control heat flow via atomic-scale engineering of the materials. In this study, thermal diodes made of single layer MoS2 nanoribbons are investigated using non-equilibrium classical molecular dynamics. Specifically, we focus on the influence of shape asymmetries of the nanoribbons on the thermal current, and obtain thermal rectification ratios up to 30% for the T-shaped nanoribbons. This behavior is then rationalized through a detailed analysis of the vibrational spectrum of the ribbons. In particular, it turns out that thermal rectification is mostly related to (i) the transversal finite size of the ribbon and (ii) to the different localization behavior of high-frequency modes for forward and backward heat flow directions. We expect our results to shed light on the potential of 2D materials for the engineering of highly efficient nanoscale thermal devices.