In Malaysia, we have this coffee served everywhere for about RM2 or 0.50USD. We call it "kopi susu", simply milk coffee. I find it creative you call it sunrise coffee, gives off good vibes.
It is served separated, with coffee on the top layer and milk at the bottom layer. Then before drinking, we stir the milk and coffee together with a spoon. Sometimes we leave a portion of the milk settle at the bottom to reduce sweetness.
In Malaysia there is another variation of which another layer of palm sugar syrup is added, which we now call Kopi 3 Layer or 3 Layer Coffee, a spinoff of 3 Layer Tea. I must say it is quite pretty.