Is some one know that for the following set $\mathbb{S}$ is there any name in graph theory?

Suppose $\Gamma$ is a simple graph and $N_{\Gamma}(g)=\{x\in V(\Gamma)|x\sim g\}$ is a neighborhood of $g\in V(\Gamma)$. Then consider

$$\mathbb{S}=\{y\in \Gamma|N_{\Gamma}(y)=N_{\Gamma}(g)\}$$

Suppose $\Gamma$ is a simple graph and $N_{\Gamma}(g)=\{x\in V(\Gamma)|x\sim g\}$ is the neighborhood of $g\in V(\Gamma)$. Then consider $$\mathbb{S}=\{y\in V(\Gamma)|N_{\Gamma}(y)=N_{\Gamma}(g)\}.$$ Is there a name in graph theory for the set $\mathbb{S}$?