In Australia using first names is the norm. Adults introduce themselves to children by their first name, the only place they call adults Mr. or Mrs. is in school. Outside of school I've only addressed the very elderly that way and only heard it used with the very elderly, such as in a doctor's office. I've wondered if this is more casual than in the US because of past interactions I've had.
The point is, you don't introduce yourself as "Mr Smith". You introduce yourself as "John Smith". People who wish to maintain a level of formality will address you as "Mr Smith" (or whatever title you hold).
Here the level of formality varies. Young-ish people commonly go for the first name only. Professional settings usually call for a higher level of formality, at least when speaking with clients/customers. But again, it depends on the situation, the people involved, the level of familiarity, etc.
In school the level of formality rises as you rise in level. In primary schools teachers and pupils are addressed by first name, while in university instructors are addressed as "Professor" and students are addressed as Mr/Ms.
Ah, but in certain settings (at least here), you do introduce yourself as Mr or Ms Smith. When I worked in corrections, we didn't allow the inmates to use our first names, so we rarely said them ourselves. "Hi, I'm Ms Smith. I'm going to be your case manager."