How To Set Privacy For Lock Screen (SMS and iMessage) Messages?

I have an iPhone 11 Pro Max running iOS 13.2.3 and I can't figure out (if it's even possible) to have better privacy for text messages on my lock screen, let me explain.

When I receive a message through Facebook Messenger or WhatsApp and my phone is locked then all I see on my lock screen is "Message" in blue/white (Facebook Messenger) or green (WhatsApp). There is no name or phone number that shows, great privacy feature.

When I receive a text message to my iPhone (SMS or iMessage) I will either see "Message" but with the person's name (if they are saved in my address book) or the entire phone number (if they aren't saved in my address book).

***Also if I recieved a text message after turning off and on my iPhone without unlocking it once then every single message shows the entire phone number (even if the contact is saved in my address book).

Apple loves to talk about privacy, privacy, privacy but these are huge privacy issues to me and I'm sure other people. This seems to be a basic feature (thus why Facebook Messenger and WhatsApp use it for example along with other apps) but I can't seem to figure out how to set it up...if it's even possible for text messages?

I have "Show Previews" turned off under the notifications for Messages in settings but nothing. I know I can turn off message notifications from showing on my lock screen but that's stupid...

Please help and thank you!