Could be kennel cough ... has he been around other dogs recently? There’s also canine flu, but that usually makes them sicker (fever etc.). If it is kennel cough, there’s not too much to be done for it - just watch to see he doesn’t get sicker and if he does bring him as they may want to put him on antibiotics to fend off a secondary infection. Or he could still have something caught in his throat or maybe even allergies (although a cough is not a common symptom in dogs). Coughs can also indicate heart failure, but probably not in a dog that young - if it was an old dog I would be more concerned. If you do end up bringing him in while he is still coughing, be sure to warn the vet in advance - they may not want him coming through the waiting room as kennel cough and canine flu are both highly contagious.