Why are C6 dispersion forces named C6?
From Calculation of Coefficients in the Power Series Expansion of the Long‐Range Dispersion Force between Atoms J. Chem. Phys. 56, 2801 (1972)


  Highly accurate calculations
  of $C_6$, the coefficient of the $R^{-6}$ term, resulting from
  an induced dipole-induced dipole interaction, have
  been made for many atomic systems, while values of
  $C_8$ (dipole-quadrupole interaction) and $C_{10}$ (dipoleoctopole
  plus quadrupole-quadrupole interactions) are...


In other words, in London dispersion interaction is usually represented as induced dipole - induced dipole interaction, the energy of which is proportional to $R^{-6}$, but there are other components of the interaction.