  We study the dynamics of (i) neutral test particles, (ii) magnetically
charged test particles, and (iii) test magnetic dipole around a regular Bardeen
black hole surrounded by perfect fluid dark matter (PFDM). It has been shown
how the magnetic charge of the black hole and the parameter of the surrounding
PFDM can influence the innermost stable circular orbit (ISCO) radius of a test
particle. We have found that the ISCO radius is strongly affected as a
consequence of the combined effect of the magnetic charge parameter and the
perfect fluid dark matter. The black hole magnetic charge parameter $g$ and the
combined effect of perfect fluid dark matter can mimic the black hole rotation
parameter up to $a/M\approx 0.9$. It has been observed that the ISCO for
magnetic dipole disappears at the values exceeding the calculated upper value
for the magnetic interaction parameter $\beta$. The upper limit decreases with
the increase of both the dark matter and magnetic charge parameters. Finally,
as an astrophysical application, we have analyzed degeneracy effects of spin of
Kerr black holes and magnetic charge of regular Bardeen black holes for the
different values of the dark matter parameter providing exactly the same value
for ISCO radius of a magnetic dipole with the same value of the parameter
$\beta=10.2$ of the magnetar called PSR J1745-2900 orbiting around supermassive
black hole Sagittarius A*.
