Most messaging apps will promise you the moon in terms of security and privacy, but the fact remains that they have your email, your identity and even your phone number. 

We seem to have no choice but to trust what they are saying as gospel truth and hope they have our best interests at heart. Unfortunately, almost every messaging service out there is there to make money, so I hate to break it to you, that means they are not giving you these services for free. So are there options where you can claim complete anonymity? Surprisingly there are a few gems. 

Session

Session is an open source, end-to-end encrypted messaging app that is focused on confidentiality and anonymity unlike mainstream apps like WhatsApp, Signal or Telegram it doesn’t need a phone number, email ID, or any ID for that matter. When you create an account, a random 66-character alphanumeric ID is created and for all purposes this is your chat ID. It supports one-to-one and group messaging with support for multimedia files. It is also super easy to install and is available on almost all platforms. Getting an ID is effortless, just go to the website and download the software and you will get an ID. The drawback is that if your ID is ever leaked it would be a problem to recover or secure as there is no 2FA. However, if you are careful with your ID, this program offers the most anonymity. 
Get it here: https://getsession.org/