I have a Moto G phone, and since sometime last fall, my phone will no longer store contacts. It seems to store “blank” contacts with no information on its own (which I later have to delete), but when I try to save a phone number from a call, text, or just add contact function, it takes it, says it is saved, but then the name is not there.
Do you have a google account? If so is it listed on your phone under accounts? If the account is on your phone then open a chrome browser and login to that account and View the contacts. They should be all there. If the contacts are there then the account isn’t syncing to the Phone.