Wally Wallet respects your privacy. No personal information is sent to Wally Wallet servers from the app. In fact, there ARE no Wally Wallet servers! To receive blockchain information, Wally Wallet accesses blockchain “full nodes”, via the standard Bitcoin P2P and Electrum protocols.
If you use the “identity” feature to perform a web site registration, Wally wallet will provide the web site with only the identity information that you have explicitly allowed it to provide.