In this paper, we propose a simple and efficient scheme for establishing anonymity in clustered wireless sensor networks. This scheme is applied to a clustered sensor network in which the nodes in a neighborhood share pairwise keys for authentic and confidential communication. The scheme, named Simple Anonymity Scheme (SAS), uses a range of pseudonyms as identifiers for a node in the network, to ensure concealment of its true identifier (ID). After deployment, neighboring nodes in the network share their individual pseudonyms and use them to ensure that the communication is anonymous and that a node's true ID is kept private. Even when many nodes in a given neighborhood of the network are compromised and are colluding, our scheme ensures that non-compromised nodes are still guaranteed complete anonymity. The compromised nodes cannot identify the sender or the receiver of communication happening between non-compromised nodes. Our scheme requires reasonably low memory and has very low computation cost, needing no change in other protocols of the network stack. It can be embedded into any wireless sensor network routing protocol to ensure anonymity and privacy during node discovery and routing in the network.