  We consider a gravastar model made of anisotropic dark energy with an
infinitely thin spherical shell of a perfect fluid with the equation of state
$p = (1-\gamma)\sigma$ with an external de Sitter-Schwarzschild region. It is
found that in some cases the models represent the "bounded excursion" stable
gravastars, where the thin shell is oscillating between two finite radii, while
in other cases they collapse until the formation of black holes or naked
singularities. An interesting result is that we can have black hole and stable
gravastar formation even with an interior and a shell constituted of dark and
repulsive dark energy, as also shown in previous work. Besides, in three cases
we have a dynamical evolution to a black hole (for $\Lambda=0$) or to a naked
singularity (for $\Lambda > 0$). This is the first time in the literature that
a naked singularity emerges from a gravastar model.
