From physics courses, I'm told that (for Hydrojen atom only), for a given $\vec L$ of the electron,
$$|\vec L| * cos(\theta) = m_l,$$ where $\theta$ is the angle between the magnetic field and the orbital angular momentum $\vec L$.
Therefore, for example, if $\vec L$ lies on the $x-y$ plane, $L_z$ should be zero. However, when we see the value of $m_l$ for, say for $p$, subshell, they are $1, 0, -1$, and generally the orbitals are named as $p_x, py_, p_z$, and this confuses me. I mean if $\vec L$ is in the $z$ direction (i.e in the direction of $\vec B$), then $m_l = \pm 1$, and if it is on the $x-y$ plane, then $m_l = 0$, but naming implies as the values of $m_l$ are matched one-to-one to the names $p_x, p_y, p_z$, so am I confusing anything here, or the problem is just a silly naming of the orbitals ?