What would you like to drink? Paraphrases

None of them are very idiomatic.
What do you want to drink now? suggests that the person has been drinking one thing but now wants to drink something different.
What do you want to drink, now? is possible, where now is a filler word like eh.
What do you desire to drink now? is old fashioned and overly formal.

In a restaurant or bar: 'May I have your drink order, please?'
At someone's home: What would you like to drink?'
At someone's home: I have red wine, coffee, iced tea, orange soda, milk and of course, water. What do you prefer?'

Blue JayWhat do you want to drink? and What would you like to drink? are the usual phrases.

Thanks! So, somehow they are interchangeable to ask someone what he wants to drink at the moment of asking.

Blue Jayand if it is alcohol being offered there is a somewhat dated phrase Name your poison.

Didn't know that one! Quite logic

AlpheccaStarsAt someone's home: What would you like to drink?'

Hi,
Is this the right one only? Isn't there a more informal one?

TL

Tenacious LearnerWhat do you want to drink? and What would you like to drink? are the usual phrases.Thanks! So, somehow they are interchangeable to ask someone what he wants to drink at the moment of asking.

Yes.

Blue JayYes.

Hi,
No further qurestions at this point.

TL