My theory:
Marowak leave their eggs after laying them. To prevent predators from finding and eating the eggs, they look like animal skulls (laying an egg must be extremely painful for a Marowak. That is, nobody have ever seen a Pokémon lay an egg, so nobody knows for sure), and are half-buried by the mother before she leaves the nest. The skull-like upper half of the egg is also extremely tough, providing the infant Cubone with what is basically a piece of armour after hatching. The rest of the egg is peeled away, but the "skull" remains with the Cubone. The same goes for the extremely nutritous bone-like structure kept inside the egg as food for the baby. The sight of baby Cubone walking around with "skulls" on their head, and no mother in sight, has led to the misconception that Cubone wears the bones of its dead mother. The skull and club eventually become a natural part of Cubone's body, causing them both to change when Cubone evolves.