You will need at least 1-foot, 9-inches (24-inches is standard) away from the back wall for hanging. When spanning an opening of more than 48-inches, consider adding a center support to the closet rod for added stability.
How do you make a closet rod support?
https://www.youtube.com/watch?v=LimIOo_cuTA
How do you anchor a closet rod?
https://www.youtube.com/watch?v=DxclAXeF1lw
Where should closet rod brackets be placed?
Mark the position on the wall for brackets: 68" from the floor to the top of the brackets for a single level closet, 42" and 82" for a bi-level closet. For safety and stability, Brackets should be spaced no more than one stud (about 32") apart on the wall and MUST be attached directly to the wall stud.
How much space should be between rod and shelf?
Leave at least 3 feet of space between the two rods. These systems usually work best for skirts, blouses, shirts or pants folded over a clothes hanger. If you want to hang shelves above a medium-height rod, position the rod at least 54 inches above the floor. Rod depth is also important.