  We propose a self-stabilizing algorithm for computing a maximal matching in
an anonymous network. The complexity is $O(n^3)$ moves with high probability,
under the adversarial distributed daemon. In this algorithm, each node can
determine whether one of its neighbors points to it or to another node, leading
to a contradiction with the anonymous assumption. To solve this problem, we
provide under the classical link-register model, a self-stabilizing algorithm
that gives a unique name to a link such that this name is shared by both
extremities of the link.
