  We study Wigner crystallization of electron systems in phosphorene quantum
dots with confinement of an electrostatic origin with both circular and
elongated geometry. The anisotropy of the effective mass allows for the
formation of Wigner molecules in the laboratory frame with a confined charge
density that has lower symmetry than the confinement potential. We find that in
circular quantum dots separate single-electron islands are formed for two and
four confined electrons but not for three trapped carriers. The spectral
signatures of the Wigner crystallization to be resolved by transport
spectroscopy are discussed. Systems with Wigner molecule states are
characterized by a nearly degenerate ground state at $B=0$ and are easily
spin-polarized by the external magnetic field. In electron systems for which
the single-electron islands are not formed, a more even distribution of excited
states at $B=0$ is observed, and the confined system undergoes ground state
symmetry transitions at magnetic fields of the order of 1 Tesla. The system of
five electrons in a circular quantum dot is indicated as a special case with
two charge configurations that appear in the ground-state as the magnetic field
is changed: one with the single electron islands formed in the laboratory frame
and the other where only the pair-correlation function in the inner coordinates
of the system has a molecular form as for three electrons. The formation of
Wigner molecules of quasi-1D form is easier for the orientation of elongated
quantum dots along the zigzag direction with heavier electron mass. The smaller
electron effective mass along the armchair direction allows for freezing out
the transverse degree of freedom in the electron motion.
