This Wikipedia page at least tries to explain the name as the stochastic interpretation of QM

> "Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by Edward Nelson [[6]]( and is called stochastic mechanics. This was also developed by Davidson, Guerra, Ruggiero and others."

Nelson developed his "dynamical theory of Brownian motion" in 1966.


And then there's this :