The most common type of shower pan is the fiberglass version, which is designed to be used in most basic bathrooms. It is waterproof, lightweight and comes in one large mold that's easy to install. The resin coating on the fiberglass allows it to be painted, as long as you use an epoxy-based paint that properly adheres to the surface and protects against water.
Adherence is your primary issue when painting a fiberglass shower. Because the pan typically has a gel coating over the fiberglass to protect it from damage, most paints will not properly adhere. Before applying the new layer of paint, remove all old grout or caulk along the edges of the shower, sand down any glossy areas and thoroughly clean the area with a strong detergent.
In some cases the shower pan is only a subfloor material designed to be used with other materials, specifically ceramic or stone tiles. The pan provides support and protection for the tile layer. In this case, you cannot paint the pan and use it without the tile. It may be a good idea to paint the pan with a primer or sealant before installing the tile.
If your shower pan has already been completed and is lined with tile or stone, you cannot paint it. You can use ceramic tile paints if you want to start a very in-depth project that requires lengthy tile preparation, but painting over normal tiles won't allow a paint layer to bond properly, and stone tile is not designed to accept a coat of paint.