I work with doctors. (the medical and dental kind, not the PhD kind).  They actually do that kind of thing.  They don't even know it comes across as obnoxious.  SHe's aware that wizards are a bit formal and don't tend to use first names that quickly.  She's also aware they don't have the title "doctor".  She thinks she's being helpful.  Hermione does that too--does things that she has no clue come across as obnoxious.