We consider the electronic spectrum near M=(π,π) in the nematic phase of FeSe (T<Tnem) and make a detailed comparison with recent ARPES and STM experiments. Our main focus is the unexpected temperature dependence of the excitations at the M point. These have been identified as having xz and yz orbital character well below Tnem, but remain split at T>Tnem, in apparent contradiction to the fact that in the tetragonal phase the xz and yz orbitals are degenerate. Here we present two scenarios which can describe the data. In both scenarios, hybridization terms present in the tetragonal phase leads to an orbital transmutation, a change in the dominant orbital character of some of the bands, between T>Tnem and T≪Tnem. The first scenario relies on the spin-orbit coupling at the M point. We show that a finite spin-orbit coupling gives rise to orbital transmutation, in which one of the modes, identified as xz (yz) at T≪Tnem, becomes predominantly xy at T>Tnem and hence does not merge with the predominantly yz (xz) mode. The second scenario, complementary to the first, takes into consideration the fact that both ARPES and STM are surface probes. In the bulk, a direct hybridization between the xz and yz orbitals is not allowed at the M point, however, it is permitted on the surface. In the presence of a direct xz/yz hybridization, the orbital character of the xz/yz modes changes from pure xz and pure yz at T≪Tnem to xz±yz at T>Tnem, i.e., the two modes again have mono-orbital character at low T, but do not merge at Tnem. We discuss how these scenarios can be distinguished in polarized ARPES experiments.