I think each state has different regulations about that. Call your State's Dept of Agriculture for the requirements locally.
Here in Ohio, if an egg carton is reused, all markings (including the date stamps on the side) must be completely covered. The carton must be in excellent, clean condition.
The labeling we use must include our farm name, date packed, classification, and egg sizes. Our label states: Mixed Sized, Unclassified with a Laid/Packed Date. (Note: More people seem to be impressed by the date the eggs were laid the day than the date they were packed. Most of our customers get eggs laid within a day or two of purchase.
)
In Ohio, if selling from my farm property, no inspection is needed. However, an inspection is required to sell our farm eggs in another county or any place in our county that is not our farm property.
Also, if selling anywhere except from our farm, eggs must be kept refrigerated at 40°F immediately after they are gathered. The eggs should be clean, but washing is not required. The inspection was free. The inspector tested my refrigerator was at correct temp and that the refrigerator was clean. He also glanced at the rest of the kitchen to see the condition it was in. The first one they set up an appointment, after that, annual inspections (if done) are by surprise visit.
More than you asked for... but I would recommend you check with your state Dept of Ag to find out the regulations. Or possibly you can find them online.