Because it takes two to tango.
Dipoles interact with each other. A Lone dipole has nothing to interact with (other than an electric field, but if we ignore some externally applied macro field, there is nothing for a lone dipole to interact with).
So molecules with an inherent dipole (like water or chloroform) interact with each other. One molecule's dipole interacts with the other molecule's dipole. So you would never say "dipole interaction" only "dipole-dipole interaction". The repeated word is because it takes two dipoles to interact.
The same pattern applies to non-polar molecules with little or no inherent dipole. For example, benzene. Benzene has no built-in dipole, but the electrons in its bonds are fairly polarisable (which basically means it is easy to induce a dipole in them). So benzene molecules do interact but via London or van der Waals forces which are much weaker than the reactions of molecules with inherent dipoles. But one way to describe those weaker interactions is (simplifying a lot) to see them as forces created by fluctuation and temporary quantum-mechanical induced dipoles. Imagine the electrons in one benzene molecule stray from perfect symmetry in their distribution and create a temporary dipole; this may interact with the electron clouds in other benzene molecules an induce other temporary dipoles (or interact with other existing temporary dipoles). Either way the interaction is an "induced dipole-induced dipole" interaction.
So however you understand the interactions, to describe them properly you have to repeat the phrase twice.