Hi Rose,
for semiconductors such as MoS2, the exact position of the chemical potential inside the gap is heavily dependent on the k-points sampling. If the Brillouin zone is undersampled, there will be an error in the position of the chemical potential, and the system will appear as doped, even if the system is still charge neutral.
Regarding the doping method, the main difference between the two methods is that in the "Explicit charge" method the extra charge redistributes over the entire unit cell, whereas the "Atomic compensation charges" method allows to localize the extra charge in some specific region of your simulation cell.
If you plan to study a transistor-like geometry of the type metal-semiconductor-metal, then the "Atomic compensation charges" is the method of choice, because it will allow you to dope the semiconductor without doping the metal, see for example:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.155302If you just want to add an intrinsic doping to a bulk material, then I would use the "Explicit charge" method.
Regards,
Daniele.