How much other traffic is there on the street we're walking down? So far I've been playing Korth as not trying particularly hard to keep his identity secret but he'd still probably stop short of blurting out "Dudz, I is a Dragonz!" to a street full of people.
A Dragonborn, and a Dire Wolf are clearly visible, what other people are out in the rain are giving you a wide birth. So unless you are yelling, or speaking really loudly, no-one outside the group is going to hear you. In-mechanical context, Listen DC 25 for the closest one, taking 10 for... less than that.
I'm assuming that the attitude of ordinary people towards dragons in this setting is pretty similar to other setting (OMFG, giant lizard monster, RUN!)
As the examples that are given in the Views from Outside section of the races. Some are more educated than that, some don't know how to react, most react like you present. Though, that goes mostly for when you are in that form, if you walked up to the average plebeian and said "hey, I'm a dragon", you'd be met with curiosity and / or confusion. The fact that dragons transfrom is reletively common knowledge, but it still isn't something that is thought about often, and if they make the connection (and don't just think you're a crazy person), then you might be met with a lot of additional fear, but they won't "Lizard Monster! Run!" unless you're in that form. Usually.
I'm just trying to play Fina from her perspective; distrustful of strangers, guarded, but still generally warm and outgoing.
Not to worry, you'll never hear Grugruk say he's a druid. 
best you might get is shaman.
[...]my friends here are Grik, my druidic companion, [...]
Hopefully the image of how he's standing in the one stirrup isn't too convoluted.
Not to me, but I've done that. I can't imagine, given the difference between doing that on a Walker compared to an Arab, how that would balance on a Dire Wolf, but I get the idea. Besides, I'm willing to bet your character is a much better rider than I at that point.
