I’m confused. When are the questions sent to your blog anonymous, and when aren’t they?
If you submit a question through the form on the Dear Coquette website by pressing the “Go ahead, be vulnerable” button, then it’s completely anonymous. I have no way of knowing who you are.
Tumblr also has an ask box feature. I don’t link to it, but the URL is fairly obvious and enough tumblr users know how to find it that I get quite a few submissions there. If you submit through the tumblr ask box by pressing the “Ask” button, it’s not anonymous, because I know which tumblr sent it to me.
I do this deliberately, of course. The tumblr ask box is sort of a back door I leave open for neighbors. (They call it the tumblr community for a reason.)