What is the standard distance a closet rod should be from the back wall?
As far as I know, there is no "standard" for this. I've looked for them. The only standards have to do with the actual closet dimensions that are specified in building codes. A common convention is 12" from the back wall to the center of the rod.

People typically put the closet rods in the middle of the closet. Minimum closet depth is 24" so that puts the closet rod at 12" too.

Certain types of clothing tend to extend past the edge of the hanger. The sleeves of jackets and dress shirts for example. So you want to have room for them. Good air circulation is also important to minimize chances of mold and mildew. Especially important if the back wall of the closet is an exterior wall.