Which sugar is called invert sugar? Why is it called so?

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Sucrose is called invert sugar. The sugar obtained from sugar beet is a colourless, crystalline and sweet substance. It is very soluble in water and its aqueous solution is dextrorotatory having. $[\alpha]_\text{D}=+66.5^\circ$ On hydrolysis with dilute acids or enzyme invertase, cane sugar gives equimolar mixture of D-(+)-glucose and D-(-)-fructose.
$\text{C}_{12}\text{H}_{22}\text{O}_{11}+\text{H}_{2}\text{O}\ \xrightarrow{\ \ \ \ \ \ \ \ \ \ \ \text{HCl}}\text{C}_{6}\text{H}_{12}\text{O}_{6}+\text{C}_{6}\text{H}_{12}\text{O}_{6}$
So, sucrose is dextrorotatory but after hydrolysis gives dextrorotatory glucose and laevorotatory fructose. D-(-)-fructose has a greater specific rotation than D-(+)-glucose. Therefore, the resultant solution upon hydrolysis is laevorotatory in nature with specific rotation. Since there is change in the sign of rotation from dextro before hydrolysis to laevo after hydrolysis, the reaction is called inversion reaction and the mixture (glucose and fructose) is called invert sugar.

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