  We report a comprehensive study of the two-phonon inter-valley (2D) Raman
mode in graphene monolayers, motivated by recent reports of asymmetric 2D-mode
lineshapes in freestanding graphene. For photon energies in the range $1.53 \rm
eV - 2.71 \rm eV$, the 2D-mode Raman response of freestanding samples appears
as bimodal, in stark contrast with the Lorentzian approximation that is
commonly used for supported monolayers. The transition between the freestanding
and supported cases is mimicked by electrostatically doping freestanding
graphene at carrier densities above $2\times 10^{11} \rm cm^{-2}$. This result
quantitatively demonstrates that low levels of charging can obscure the
intrinsically bimodal 2D-mode lineshape of monolayer graphene, which can be
utilized as a signature of a quasi-neutral sample. In pristine freestanding
graphene, we observe a broadening of the 2D-mode feature with decreasing photon
energy that cannot be rationalized using a simple one-dimensional model based
on resonant \textit{inner} and \textit{outer} processes. This indicates that
phonon wavevectors away from the high-symmetry lines of the Brillouin zone must
contribute to the 2D-mode, so that a full two-dimensional calculation is
required to properly describe multiphonon-resonant Raman processes.
