There are many names for the same objects that is known as the Arens--Eells spaces, transportation cost spaces, free Banach spaces over a (pointed) metric space, and Lipschitz-free Banach spaces.

The last one bothers me a bit. Doesn't the construction something-free mean free of that something? Think of alcohol-free drinks. The name free in Mathematics means free of further relations, so the name means free of Mr Lipschitz, who's been quite dead for some time already.

Is it just slopiness or is there are good reason to call these spaces Lipschitz-free?