Have any of you other SD people had to do publicity when you got your dogs?
Nup.
I got asked to have my dog appear as Miss December (sorry, Mr December doesn't have the same ring to it!) in a fundraising calendar (without me). Sure. Here's a pic of my dog - go nuts.
The organisation I'm with keep a FB page, and routinely celebrate graduates (ie the dog, not the person!) through the program by posting a pic and a congratulations on the page. But the FB page is largely for the extended family that those of us who have been assisted by the organisation like to call it.
They have a very limited number of past dogs pics on their website, and the only disabled person who appears on the page (to my recollection) is one of the trainers, who is an amputee.
None of the current dogs or handlers appear on the GoFundMe page which coordinates the public fundraising.
I do remember the first organisation I contacted about training my own dog sent a publicity authority/waiver for me to sign which had no specific limit on when or where pictures might be taken or used. I was simply asked to agree to them using my image whenever they wanted.
It was one of the many documents that I refused to sign for that organisation and ultimately didn't use them.
The situation with you and your dog may be different though. Will you own the dog? Or do they retain ownership? That may impact the way they use images of their dog.
But not pics of you. Perhaps suggest that you'd prefer time to get settled and confident with your dog as a team before "outing" yourself publicly as an Assistance Dog handler?
If they continue to own the dog? Then yeah, images of this dog being a huge success and life changer for you is going to be an important part of their ability to raise funds moving forward.
But not you and your identity. Nah.
Perhaps you could even suggest that you'd be happy to make the dog available to them when they want to do any publicity, but to stand aside and not personally appear in that publicity for now?
If all else fails, "I can't keep a public profile, such as a Facebook or Instagram page for personal safety reasons". Usually shuts people up. If they own the dog? The dog is one of their heros. Doesn't mean you personally need to appear.
Also doesn't rule out your assisting with marketing/publicity in other ways, so long as your identity is protected.