Trust? That seems to be reaching a bit.
Unless you're writing non-fiction, what is there to trust?
No one cares who I am. I'm just a name on a cover of a book of made up stories. I could change the name every other book and it would probably make no difference, except to those few who may enjoy my writing style and look for the name in case there is another book that matches the style. They're not looking for me the person. They're looking for a similar reading experience. The name is about as important as the brand name on a bar of soap.
In your world perhaps it is important, but for most readers? I doubt they give two whits about the author. You're just a name on a cover. A bunch of pixels on a screen. That's all.
**Note I am not talking about pen names. I have a pen name, largely because my real last name is unpronounceable and unspellable. It starts with three vowels in a row. (My first name is the same; my last name is an Anglicized version of my real name.) I am talking about making up a persona and interacting as it.**
In romance, many readers DO "get to know" the author as a person through her books. That is actually pretty common in such a character-driven genre, where the whole book is about two people's journey to be a better version of themselves. When a romance author sells well, many readers DO care who she is.
I was surprised also, after I published, that people wanted to interact with me on Facebook and so forth, that they wrote to me. I didn't start a newsletter for a couple years (pretty dang stupid of me), partly because I couldn't imagine they'd really be that interested in whatever I'd put in there, beyond "New book's out." But they are. They (not all of them, but a fair number) feel a connection through what I have written. This is not at all uncommon in this genre.
The best part is that those are the readers who will follow you across subgenres. They are not looking for a generic fix of HEA. They are looking for the way *you* write about people, for *your* insight and *your* humor and *your* compassion. Which makes lying to them about who you are in order to draw them deeper into a sort of cult of personality and take advantage of that desire--well, kind of a dick move.
That doesn't mean you have to share all of yourself, or all the details of your life. It just means that whatever you share is authentic.
It is like knowing anybody, I suppose. If you find out that your neighbor's whole story, under pretense of which she has conned you out of time and sympathy and groceries, is a lie--that's a betrayal. And if you find out that somebody you've come to like a lot online is somebody else entirely, that they've been concocting a persona and interacting with you as it in order to sell you something, especially in order to sell you on their worldview that focuses on kindness, generosity, etc.--that feels crappy. The person feels stupid.
I suppose there are two kinds of people. The kind who would feel awful about doing something like that, and the kind who puts the blame on the "buyer." "They shouldn't believe everything they hear about somebody online." "I'm doing them a favor, really, opening their eyes." I can't spin it that way. It's still wrong, even if the person was too trusting. You're taking advantage of their trust, and that's just WRONG.