Issues with popular messenger apps
Telegram and Signal are the most popular privacy oriented messenger apps. However, both require you to yield a very import privacy identity vector, your phone number. Hence, anonymous here refers to cutting out the phone number requirement.
Moreover, the owner of Telegram Pavel Durov is a member of the World Economic Forum. Signal contains closed source code and the owner Moxie Marlinspike is of that ethnicity that is the greatest enemy of free speech, but I digress.
Facebook messenger and WhatsApp (also owned by Facebook, Meta) are secure in the sense hackers can't easily read along. But if you think Facebook isn't reading along, I think you're sadly mistaken though I have no proof of this.
To acquire that anonymity, some convenience will have to go but it's not that bad.
Instead of using phone numbers or e-mail addresses, Session uses unique identifiers. A long string of text much like a Bitcoin address.
Download Session messenger to get started on your phone, desktop or both.
I think F-Droid is the best installation method because then Google doesn't know about you having Session and who knows what else they're up to. The F-Droid route does involve a few minor extra steps. All other options will work fine too.
Calling reveals IP-address
Phone calls reveal the IP-address to your correspondent and to Oxen nodes. A workaround could be to connect to Tor first and then start Session inside a Tor session. Calling is still in beta at the time of writing.
Session messenger uses the Oxen blockchain in the background. An ox is a male bovine, often a neutered bull or a steer. Moloch is an ancient deity that required child sacrifices and was represented as a bull.
Sure, you can say "an ox is a working animal, that's why" which is true, that said, I would never chose a bull or an ox for exactly this reason.
There's also "lokinet". A quick search on the webs yields, a Norse deity, a cunning trickster who had the ability to change his shape and sex (transgenderism). God of chaos, lies, starts fights...
To conclude, the ones choosing these names in the background at the very least glorify dark figures.