I like Philip's answer to your question. If you were to provide the entire context, we might have some more options. Jasmine, is there something special that you say in Vietnamese?

Not really. For people sleeping in the same house as you, you could say "sleep tight" or "sweet dreams", but this is very informal. Goodnight is best.

Sometimes people might say: “Night night” “Sleep well” “I’m off to bed” “I’m going to sleep” “Sweet dreams” Hope this helps! ☺️

As Philip suggested this is the only formal way. Less formal ways are…. You would initiate with Good night I am off to bed Night night I am going to hit the sack ( you are not wishing a good night, but informing them you are going to bed, but it would be replied to.) And can reply saying: Good night Sleep well Sweet dreams Sleep tight Night night Don’t let the bedbugs bite

Hope the bugs don’t bite.