Is it normal for my newborn to be losing hair?

Thanks for asking! Babies can lose hair on the back of their head by rubbing their head on the crib or bassinet.
Yes. A normal young baby can lose some hair, especially if the baby rubs the back of his head on the bed when moving his head side to side. The back of his head can end up a bit bald. Cradle cap rash on the head can also lead to hair loss, as the hair can fall out as the cradle cap flaky crust is removed from the scalp. Show the scalp to the doctor at the next check up to be sure it looks normal.
Yes. Newborns lose their baby hair at about 3-4 months of age. It is replaced by thicker, coarser hair. Some infants will develop "bald spots, " where the hair growth is very thin until the new hair regrows. These spots are now more common on the back of the head in many infants due to lying them on their back to sleep, and putting them in reclining safety seats.