Nowadays, a majority of apps require you to sign up with your email or even worse your phone number. If you have a phone number attached to your name, meaning you went to a cell service/phone provider, and you gave them your ID, then no matter what app you use, no matter how private it says it is, it is not private. There is NO exception to this. Your identity is instantly tied to that account.
Signal is not private. I recommend Simplex or another peer to peer onion messaging app. They don’t require email or phone number. So as long as you protect your IP you are anonymous

Privacy and anonymity is different things
When this US service has your phone number (meaning your real name and address), then what is the point of making this distinction? Is them having my address private?
No one should have this info, regardless of how you every person differently defines “privacy” vs “anonymity”
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So its a “private” and “secure” US corporation that knows everyone I talk to and when? I’ve heard this one before.
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This means nothing when you have no idea what code the server is running, they even went a whole year without publishing their server code updates, until they got a lot of backlash over it. Real security doesn’t require a “just trust us” claim.
Also, metadata is content. Even if they don’t have the message text, Signal still has the real identities of everyone you talked to, and when. With that you can build social network graphs, which are far easier to harvest and more useful anyway than trying to read through message content and determine meaning.
Just because you know where I live doesn’t mean you know what’s going on in my house
See the difference?
Words have meaning
Signal knows the real identities of everyone you talk to, and when. Is that not “knowing what’s going on in your house?”
The post office knows where I live too. And who I send messages to. Didn’t mean they read my mail