On mobile there are various options. The apps which are likely to be most secure are ones which have end-to-end encryption enabled by default and which can also be onion routed via Orbot. End-to-end encryption secures the content of the message and onion routing obscures the metadata, making it hard for a passive adversary to know who is communicating with who.
Secure and private? Signal. It is not anonymous, though. And it can be a potential metadata honeypot later, even if it is not one right now. See recent Anom scam.
Secure, private and anonymous? XMPP. Matrix. Briar. Retroshare.
There are parts of the world, like 80% of it I guess, where secure=anonymous.
Encryption does not hide your identity, necessarily, as far as instant messaging goes. Different aspects.
80%?! What magical planet are you from? This is complete nonsense, put some sources because this is a complete lie. Nobody will believe you without proof.