There are two domes

For more than 650 years after the Prophet ṣallallāhu 'alayhi wa sallam (peace and blessings of Allāh be upon him) passed away, there was no dome over his ṣallallāhu 'alayhi wa sallam (peace and blessings of Allāh be upon him) grave.  The first one was built in 1279 by a Mamluk sultan and was made of wood.  The green dome that we see today is actually the outer dome over the room of the Prophet ṣallallāhu 'alayhi wa sallam (peace and blessings of Allāh be upon him). There is an inner dome that is much smaller and has the name of the Prophet ṣallallāhu 'alayhi wa sallam (peace and blessings of Allāh be upon him), Abu Bakr raḍyAllāhu 'anhu (may Allāh be pleased with him) and Umar raḍyAllāhu 'anhu (may Allāh be pleased with him) inscribed on the inside.