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 $2times 10^{11} rm cm^{-2}$. 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.
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