I've always used Harmonic Sum for xy/(x+y). I can't say what "standard" is. It does violate the heuristic that any kind of sum operation should exceed its inputs.

(x+y)/(1+xy) might be called the "relativistic sum" of x and y (since this is how velocities add in special relativity). Does this operation arise in other places? Note that (x+y)/(1+xy) = tanh (arctanh x + arctanh y). Jim Propp