SimpleX might be worth a look. Although, I think the developer eventually wants to pursue a two-tiered business model. Otherwise, for something like Matrix (where there are several client apps available), no-one's forcing you to give over your actual details.
What you want to do exactly cos i know an app called Session but idk exactly what you mean with "Anonymous", if you want some kind of app like WhatsApp but for securely communication I suggest you that app.