I could not tell if the woman in the exchange pronounced Do or dropped it when she asked the man about his name; I could not hear the word Do at all. For all I know, whoever transcribed the conversation might have added Do. Then it came to mind whether there is any difference in tone/stress between:
Good, strong name. [Do] your friends call you John or Jack?*
Good, strong name. Your friends call you John or Jack?*
The sentence is part of the exchange below from Vertigo 1958.
Thank you But I don't know you, and you don't know me
My name is Madeleine Elster
My name's John Ferguson
Good, strong name. Do your friends call you John or Jack?
Oh, John, mostly
Vertigo 1958
Edit:
Bold Do was replaced by [Do] between brackets to help improve readability. No intention of adding stress to the sentence.