I didn't know there's any private way to talk, I only know of discord for Hive but honestly I don't go there at all.

I can only talk about Hive Keychain as that is the only thing I use. When you are on Hive, using the Chrome/Firefox extension on your computer, what you can do is to go to the "send"-tab, enter the recipient of your message, enter 0.001 HIVE as the amount (or anything else you want). Then you can enter the memo below. If you click the binary symbol (010110100) besides that, the message will be sent encrypted, so only you and the recipient can read it.
On the Android App of Hive Keychain the process is similar. There is no "send"-tab as on Firefox, but you have to go there via choosing the currency (for example HIVE) beforehand. After that, same process.

But knowing when you received such a message is quite hard. You would have to monitor your incoming transactions to know when there is a message among them, as there is no notification for incoming messages. So yea, Hive messaging is somewhat on the lower end of useful things on Hive.