title_body: Is there a name for this drink?
upvoted_answer: This sounds Cortado or Noisette to me. Still, additional water makes it a bit interesting. I assume you may simply order your coffee based on lungo instead of doppio.
  
  Again, lungo based Cappucino Scuro may be another alternative. However, it also has foam on top of steamed milk.
  
  This answer includes so much terminology. So, let me make a glossary.
  
  
  Espresso: 30 ml shot of beverage made with 8 grams of beans out of espresso machine. Our main unit.
  Doppio: 60 ml of beverage made with 16 grams of beans. Double shot espresso.
  Lungo: ~60 ml of beverage made with 8 grams of beans. Long shot single espresso.
  Cortado: A bit of steamed milk (~30 ml) is added on top of doppio.
  Noisette: A bit of hot milk (~30 ml) is added on top of doppio.
  Cappucino: A bit of steamed milk (~60 ml) then some foamed milk (~60 ml) is added on top of doppio.
  Cappucino Scuro: Same cappucino, less milk (~30 ml each). Sometimes only with foamed milk (~60 ml).