Citing Wikipedia's article on polar coordinates...
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point [pole] and an angle from a fixed direction [polar axis].
$x = r\cos{φ}$
$y = r\sin{φ}$
$r = \sqrt{x^2 + y^2}$
$φ = \arctan2{(y, x)}$
The article expounds further in the below image, with $O$ being the pole and $L$ being the polar axis.
Is it possible to change the coordinate system's pole and/or polar axis (e.g., setting $-L$ as the polar axis)?
Yes this is possible, and is in fact done all the time. If you want the pole to be at $(x_0,y_0)$ you just make the following substitutions in your equations.
$$ x \rightarrow x-x_0$$ $$ y \rightarrow y-y_0$$
Edit: To answer the question about changing the polar-axis.
One way this can be done is by rotating the coordinates so that the $x-axis$ is at an angle to what it used to be. To rotate the coordinates by and angle $\theta$ apply the transformation,
$$ x' = x \cos(\theta) - y \sin(\theta) $$ $$ y' = x \sin(\theta) + y \sin(\theta) $$
In that case what you would want to substitute into the polar coordinate equations is,
$$ x\rightarrow (x-x_0) \cos(\theta) - (y-y_0) \sin(\theta) $$ $$ y \rightarrow (x-x_0) \sin(\theta) + (y-y_0) \sin(\theta) $$