I was told that after the PS4 update 8.00 the parties will be listened to and you can be named, is that correct?

I downloaded the software update on the ps4 on October 14, 2020, and the servers were down, you couldn't start any parties, and if so, only alone, and and and. I noticed that after the update, the Sony parties were bugged and you could be banned if you were insulted or threatened, etc. But is that true? What do you think? Because these theories have been around since the ps4 came out!

No, that was a misunderstanding. Sony has already commented on this.

https://mobile.twitter.com/AskPS_UK/status/1316379000604954624

It was about a pop-up message on the Playstation, in which it was warned that the conversations could be recorded. However, this refers to a new function that party members can use to record the conversations, just like you know from Teamspeak and the like.

https://www.pushsquare.com/news/2020/10/sony_we_do_not_record_ps4_party_chats

It's not as far-fetched as you might think. For example, Microsoft has been listening and recording through the Kinect microphone on Xbox for many years. Everything about e.g. Improve Cortana and collect data. Kinect has since been discontinued.

Amazon, Google and Apple have also done this, but are now refraining from such practices due to criticism.