We theoretically study, through combining the density functional theory and an unfolding technique, the electronic band structure and the charge doping effects for the deposition of potassium (K) on multilayer FeSe films grown on SrTiO3 (001) surface. These results form a theoretical base line for further detailed studies of low-temperature electronic properties and their multiway quantum engineering of FeSe thin films. We explain the Fermi surface topology observed in experiment and formulate the amount of doped electrons as a function of atomic K coverage. We show that the atomic K deposition efficiently dopes electrons to top layer FeSe. Both checkerboard and pair-checkerboard antiferromagnetic (AFM) FeSe layers show electron pockets at M point and no Fermi pocket at $\Gamma$ point with moderate atomic K coverage. The electron transfer from K adsorbate to FeSe film introduces a strong electric field, which leads to a double-Weyl cone structure at M point in the Brillouin zone of checkerboard-AFM FeSe. We demonstrate that with experimentally accessible heavy electron doping, an electron-like Fermi pocket will emerge at $\Gamma$ point, which should manifest itself in modulating the high-temperature superconductivity of FeSe thin films.