Which term describes the amount of heat needed to change 1 kg of a substance from solid to liquid at its melting point?

This is specific latent heat of fusion.

This is the heat needed to turn 1 kg of solid into a liquid at its melting point. When a substance changes its state from  solid to liquid form or from liquid to gas , heat energy is needed. This energy is used not to heat the substance but to separate the molecules from each other.

This energy is called latent heat energy. While a liquid is boiling and while a solid is melting, there is no temperature change. The temperature only changes when the change of state is complete.