I think the girlfriend is being sarcastic. If someone is 'bright-eyed', they are alert and energetic. You would call someone 'Bright-eyes' who looked alert in this way. However, if I saw someone in the morning who looked like they wanted to go back to bed, I might say "Hello, Bright-eyes!". It would be sarcastic and the name would be a joke because they are so sleepy. I think the line that is spoken when she sets the coffee down is: "Here you are (here is your coffee) Bright-eyes!" It is her way of saying "You look like you really need this coffee to wake you up."

I think the phrase is "bright eyes". http://www.thefreedictionary.com/Bright+Eyes