In group theory (abstract algebra), is there a special name given either to the group, or the elements themselves, if x^2=e for all x?

There is a special name given either to the group, or the elements themselves, if ${\displaystyle x^2=e}$ for all x. In group theory, there are certain group which named as finitely or infinitely generated group. Here, some few examples: Boolean group (which all elements has self-inverse)
Let ${\displaystyle G=(Z_2,+)}$ be group whose all elements has order one or two. Then with the help of group G we can construct the new group named finitely generated group G’ has elements whose order is either one or two such that
${\displaystyle G^{\prime }={\mathbb{Z}}_2\times {\mathbb{Z}}_2\times {\mathbb{Z}}_2\times \dots \times {\mathbb{Z}}_2}$
${\displaystyle \leftarrow }$ n-times ${\displaystyle \to }$
Again, with the help of group ${\displaystyle G=(Z_2,+)}$ we can construct new group named infinitely generated group named S’ has elements whose order is either one or two such that
${\displaystyle S={\mathbb{Z}}_2\times {\mathbb{Z}}_2\times {\mathbb{Z}}_2\times \dots \times {\mathbb{Z}}_2}$
${\displaystyle \leftarrow }$ infinite-times ${\displaystyle \to }$
There are some group named as Klein’s group which is finitely generated group.
${\displaystyle K=\{e,a,b,ab\}}$