Except most of us are not in the military and go by our first names instead of surname. Even taking the inquisitor out of the equation, it definitely makes no sense for your close friends/LIs to be referring to you as Hawke, particularly when you have plenty of family around, or for your companions in Origins to refer to you as Warden, particularly when you have other wardens around.
While it was predominate in the military, it also happened in school. I have a very common name, obviously, Robert. In school, and in my group of friends, where we had 3 Roberts, it was easier to keep track. There is nothing immersion breaking about it to me, since I still have people in my life that "forgot" I had a first name, and even my first wife tended to call me by my surname, at times. When she used my first name most of the time, I knew I was in trouble for something...
ETA: I'm not fully understanding the using it to differentiate saves argument either. This can easily be fixed with a default name if they let you edit the name of the collection of saves for each character rather than relying on the character's name to differentiate them (IE: Name the collection of saves for one character, "Canon," another "Mage Romance Iron Bull," etc). I get that some people see it as somehow integral to their RP experience, but the "I use it to differentiate" saves argument seems like a logical fallacy as it can easily be overcome and I'm sure the devs would take that into account if they were to take away first name customization. Or they could just display save file collections by a character's avatar instead of the name so you'd easily know which character is which. See, easy. Lots of ways around it.
So to accommodate your desire, they should make it where we have to do more "work", editing save files, so that you can have a fixed first name? When I create a character, I create a unique first name, it's part of the process. When I intended to do a rift mage, I named it Riftina, so that I could differentiate it from my KE. I have 7 games running, some completed, and it's sure a lot easier for me to go down the names when I feel like playing a certain one. I'm not keen on the idea of all my characters being Will or Wilamina in order to accommodate someone else's idea of what dialog in a game should be, especially when this argument was presented in ME, where Commander would be the usual goto name, and Shepard, or a variant, was the nickname used by the main crew/close friends. I don't find it odd at all, given my military experience, that people would actually do that.