The MC for our most recent series, girldragongizzard, lives in current day (the story is happening Right Now - though it fluctuates between a few days behind to a few ahead as we're writing it and time flows narratively).
But part of the story is that the magic that made Meghan transform into a physical dragon also made it so that people accept her as what she is without fear or trepidation - she is, to the people who know her and to most strangers, a symbol of her neighborhood's power and connection to the world. She is a representative of her neighborhood's collective personality.
So, if you saw her, you'd think, "Oh. Yeah, she's just your typical downtown Fairportian manifested as a dragon. Bet she wants some coffee." And you'd be right.
She's queer, autistic but won't admit it, loud, semi-verbal and uses AAC, a great conversationalist anyway, territorial, eats seagulls when she can't afford ground chuck, sleeps on the roof of a low-income apartment building, and is possessive and protective of her people. Pretty much just like anybody you might run into on the street, but covered in scales and capable of breathing fire actually. She would give you a light if she had that much control over her flame or could operate a lighter.
Now, if you weren't affected by the magic of the story, you'd think, "Holy crap, that's an actual dragon." Her personality probably wouldn't come into play for quite some time.
The other place you're likely to run into her is online, such as on Tumblr, in which case: Oh, she's a typical 50 year old trans girl therian tumblrina pretending to be a dragon as a bit. It's not a bit.