We use scanning tunneling microscopy to visualize and thermal desorption spectroscopy to quantitatively measure that the binding of naphthalene molecules to graphene (Gr), a case of pure van der Waals (vdW) interaction, strengthens with $n$- and weakens with $p$-doping of Gr. Density functional theory calculations that include the vdW interaction in a seamless, ab initio way accurately reproduce the observed trend in binding energies. Based on a model calculation, we propose that the vdW interaction is modified by changing the spatial extent of Gr's $\pi$ orbitals via doping.
