Single-differential cross section predictions for top quark pair production are presented at next-to-leading order, using running top quark mass renormalization schemes. The evolution of the mass of the top quark is performed in the MSR scheme $m_\mathrm{t}^{\textrm{MSR}}(\mu)$ for renormalization scales $\mu$ below the $\overline{\textrm{MS}}$ top quark mass $\overline{m}_\mathrm{t}(\overline{m}_\mathrm{t})$, and in the $\overline{\textrm{MS}}$ scheme $\overline{m}_\mathrm{t}(\mu)$ for scales above. In particular, the implementation of a mass renormalization scale independent of the strong coupling renormalization scale and factorization scale in quantum chromodynamics allows investigating independent dynamical scale variations. Furthermore, the first theoretically consistent extraction of the top quark MSR mass from experimental data is presented.