The mixing of two or more atomic orbitals of similar energies on the same atom to produce new orbitals of equal energies is called?

Honey, that's called hybridization. It's like when you mix different types of alcohol to make a fancy cocktail - you get something new and exciting. So, in the world of chemistry, hybridization is the party where atomic orbitals mingle and create some fresh orbitals of equal energy. Cheers to science!