What is the name of the reaction when you split a disaccharide? what products do you gain?

The reaction is called hydrolysis. They produce 2 monosaccharides.

In hydrolysis, disaccharides, which is 2 monosaccharides combined from the opposite reaction called condensation, is broken down back into 2 monosaccharides, the simplest form of sugar, using a water molecule.

For example, Maltose, which is a disaccharide, will be broken down into 2 glucose molecules, which are monosaccharides.