We perform DFT calculations with different hybrid (ωB97X-D and M05-2X) and double hybrid (B2PLYP-D3 and ωB2PLYP) functionals to characterize the lowest energy triplet excited states of naphthalene monomer and dimers in different stacking arrangements and to simulate their absorption spectra. We show that both excimer and localized triplet minima exist. In the former, the spin density is delocalized over the two monomers, adopting a face-to-face arrangement with a short inter-molecular distance. In the latter, the spin density is localized on a single naphthalene molecule, and different minima or pseudo-minima are possible, the most stable one corresponding to a slipped parallel arrangement. According to B2PLYP-D3 calculations, excimer minima are the most stable, in line with the indications of ADC(2) studies. However, the relative stability of the minima is reverted when including thermal and vibrational effects. Excimer minima exhibit a very intense absorption spectrum, peaking above 500 nm. The computed absorption spectra of localized minima significantly depend on the stacking geometry and do not coincide with that of isolated naphthalene. Hybrid functionals provide very accurate vibronic absorption spectra for naphthalene monomer, both in the singlet and in the triplet state, but underestimate the stability of the excimer triplet.