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We present a theoretical study of the near-field radiative heat transfer (NFRHT) between two β -GeSe monolayers, each at a different temperature. (This is a relevant 2D material with superior electron transport and optical properties compared to black-phosphorus monolayers). The required optical conductivity of the monolayer is calculated using density functional theory including spin-orbit coupling, and using the Perdew-Burke-Erzenhof parametrization. Both the intra and interband transitions are taken into account, as well as the contribution of the optical phonons. This allows us to obtain more realistic predictions of the NFRHT between two monolayers of GeSe. The role of the electron doping concentration and the plasma relaxation frequency is investigated, showing a non-monotonic dependence on the radiative heat transfer with increasing doping, and having an optimal doping where the heat flux is maximize. A strong optical anisotropy in the electric conductivity is obtained from the contribution of both electrons and ions This anisotropy is explored, showing that the relative rotation of two monolayers results in modulation of the NFRHT much larger than previously found for similar 2D materials, like α -GeSe. As the angle of rotation between the monolayers increases the total heat transfer decreases. Our analysis demonstrates the relevance of properly taking into account the materialelectronic and ionic contributions. [ABSTRACT FROM AUTHOR]