Name of an Exact Cover by 3 sets variant Exact cover by 3-sets is $\sf{NP}$-complete:


Instance: Given a finite set $X = \{ x_1,x_2,...,x_{3n}\}$ of $3n$ elements and a collection $C = \{ ( x_{i_1}, x_{i_2}, x_{i_3}) \}  $ of $m$ 3-elements subsets of $X$;
Question: Find a subcollection $C'$ of $C$ such that every element in $X$ is contained in exactly one member of $C'$.


The problem remains NPC even if we add the following condition:


every element of $X$ appears exactly in three subsets of $C$


Has this variant an "official" name?
Gonzalez called this variant RXC3, for "Restricted Exact Cover by Three Sets."