What is the name of this combinator?
This isn't probably a standard name, but in The Implementation of Functional Programming Languages in Section 16.2.4 Simon Peyton Jones calls it S'. It is defined as an optimization combinator

S (B x y) z = S' x y z


The following example is from the mentioned section. Consider

λx_n...λx_1.PQ


where P and Q are complicated expression that both use all the variables.
Eliminating lambda abstractions leads to quadratic increase of term sizes in n:

P Q
S P1 Q1
S (B S P2) Q2
S (B S (B (B S) P3)) Q3
S (B S (B (B S) (B (B (B S)) P4))) Q4


etc., where Pi and Qi are some terms. With the help of S' this gets only linear:

P Q
S P1 Q1
S' S P2 Q2
S (S' S) P3 Q3
S (S' (S' S)) P4 Q4