The units used for gravitational potential energy are the units of energy, which in the International System of Units (SI) is the joule. The name of the unit is "joules" when writing it fully, not the symbol "J".

Gravitational potential energy is energy due to an object's position in a gravitational field, and its SI unit being joules is consistent with it being a form of energy.

Thus, the unit name for gravitational potential energy is: joules.