why the splited orbitals were named as eg and t2g?
We know that in the absence of an external magnetic field, all the five d-orbitals are degenerate but split into two sets of t2g and eg orbitals in the presence one. 'g' here stands for gerade, which means that the orbitals are symmetric with respect to the centre of symmetry. The t2g set of orbitals consists of three degenerate (that is having same energy) orbitals while the eg set consists of two degenerate orbitals. There is a branch of science called group theory, according to which, 't' stands for triply degenerate and 'e' stands for doubly degenerate.This is why the set with three degenerate orbitals is called t2g while the set with that with two degenerate orbitals is called doubly degenerate set.
You will learn more abut group theory in higher grades.