We present full quantum-mechanical calculations of the hybridized plasmon modes of two nanowires at small separation, providing real-space visualization of the modes in the transition from the classical to the quantum tunneling regime. The plasmon modes are obtained as certain eigenfunctions of the dynamical dielectric function, which is computed using time-dependent density functional theory (TDDFT). For freestanding wires, the energy of both surface and bulk plasmon modes deviate from the classical result for low wire radii and high momentum transfer due to effects of electron spill-out, nonlocal response, and coupling to single-particle transitions. For the wire dimer, the shape of the hybridized plasmon modes are continuously altered with decreasing separation, and below 6 A˚, the energy dispersion of the modes deviate from classical results due to the onset of weak tunneling. Below 2-3 A˚ separation, this mode is replaced by a charge-transfer plasmon, which blue shifts with decreasing separation in agreement with experiment and marks the onset of the strong tunneling regime.