H^3 perhaps. There is a precedent. The Lenstra-Lenstra-Lovasz algorithm (LLL) is often called L^3, admittedly because the complexity is O(L^3) in the bit size L. Later a quadratic algorithm was discovered, cheekily called the L^2 algorithm. Later still it was done in quasilinear time. Unfortunately, the authors of those papers did not have the sense to have names starting with L.
I also enjoyed how they went from: Heinze, Hubrich, and Halfmann -> H and H and H -> the three H's. I kind of expected it to go to "triple H"