What is a free name in a process algebra?

There are two popular approaches to specifying the semantics of process algebras: labelled transition semantics and reaction semantics. While the notion of free name is rather unproblematic for labelled transition semantics this is not so for reaction semantics in the presence of a structural congruence for unfolding recursive declarations.We show that the standard definition of free name is not preserved under the structural congruence. We then develop a fixed point approach to the set of free names and show that it is invariant under the structural congruence.