Clearly, there is an enormous freedom in how pseudopotentials are constructed. Hoever, a sistematic, first-principles method to contruct pseudopotentials is highly desirable. Clearly, a requirements is that the pseudopotential should coincide with the actual potential outside the core region. But suppose tha the wave-function obtained with the pseudopotential differs from the actual one in the core region. That means that their respective charges will be distributed differently among core and valence regions, resulting in their norms being different. This charge difference is called orthogonality hole, and should be corrected for.
Different approaches have been used in the past construct pseudopotentials. This is a complicated problem and a whole topic to study separately.
See Thijssen's book for guidelines to build a self-consistent pseudo-potential.