Anonymous shared memory is a memory in which processes use different names for the same shared read/write register. As an example, a shared register named A by a process p and a shared register named B by another process q can correspond to the very same register X, and similarly for the names B at p and A at q which can correspond to the same register Y = X. Hence, there is a permanent disagreement on the register names among the processes. This new notion of anonymity was recently introduced by G. Taubenfeld (PODC 2017), who presented several memory-anonymous algorithms and impossibility results. This paper introduces a new problem, that consists in "de-anonymizing" an anonymous shared memory. To this end, it presents an algorithm that, starting with a shared memory made up of m anonymous read/write atomic registers (i.e., there is no a priori agreement on their names), allows each process to compute a local addressing mapping, such that all the processes agree on the names of each register. The proposed construction is based on an underlying deadlock-free mutex algorithm for n ≥ 2 processes (recently proposed in a paper co-authored by some of the authors of this paper), and consequently inherits its necessary and sufficient condition on the size m of the anonymous memory, namely m must belong to the set M (n) = {m : such that ∀ ℓ : 1 < ℓ ≤ n : gcd(ℓ, m) = 1} \ {1}. This algorithm, which is also symmetric in the sense process identities can only be compared by equality, requires the participation of all the processes; hence it can be part of the system initialization. Last but not least, the proposed algorithm has a noteworthy first-class property, namely, its simplicity.