Is there a name for this?

Question

Let $G$ be a topological group.

Let $U$ be an open neighborhood of the identity in $G$. It is well known there exists another open neighborhood of the identity $V$ in $G$ such that $V\cdot V\subseteq U$.

Is there a name for $V$?

Answer 1

No.

At least, I've never heard of a name for this concept, and I am fairly certain there is no standard name for it.

This is a very old question, but I decided to give my 2 cents for what it's worth anyway.