Let $G$ be a graph and $H$ be a (not neccessarily induced) subgraph of $G$ with vertices $a,b,c,d$ and edge $ab$. $G$ is now transformed by replacing edge $ab$ in $H$ with edges $ac$ and $bd$. So our subgraph is changed from $K_2+2K_1$ to $2K_2$. This transformation is crucial in Akiyama's proof from 1983 that for every given graph $G$, a $\Delta G$-regular graph $H$ containing $G$ exists (see here).
Does this transformation have a specific name in the literature? Because I need to provide an name and would rather use a familiar one than making up my own.