  We demonstrate how hybridization between a two-dimensional material and its
substrate can lead to an apparent heavy doping, using the example of monolayer
TaS$_2$ grown on Au(111). Combining $\textit{ab-initio}$ calculations, scanning
tunneling spectroscopy experiments and a generic model, we show that strong
changes in Fermi areas can arise with much smaller actual charge transfer. This
mechanism, which we refer to as pseudodoping, is a generic effect for metallic
two-dimensional materials which are either adsorbed to metallic substrates or
embedded in vertical heterostructures. It explains the apparent heavy doping of
TaS$_2$ on Au(111) observed in photoemission spectroscopy and spectroscopic
signatures in scanning tunneling spectroscopy. Pseudodoping is associated with
non-linear energy-dependent shifts of electronic spectra, which our scanning
tunneling spectroscopy experiments reveal for clean and defective TaS$_2$
monolayer on Au(111). The influence of pseudodoping on the formation of charge
ordered, magnetic, or superconducting states is analyzed.
