I wish dialogue UI was cleaner.

[Gothicshark]

You can do that on PS4 with the Square button - it hides everything except the dialogue box and overhead names, though it resets whenever a character does an emote so you might have to hit it a few times per conversation.

I assume there's an equivalent button for PC but I wouldn't know what to try.

(It's not the same thing as hitting Scroll Lock to hide the entire UI - that's L1+ Touchpad for us.)

I have it bound to [scr lk] "Scroll Lock"