I think that the story Thnetosis in Demon: Interface demonstrates how Covers work wonderfully. I highly recommend this story if you want to understand a Demon getting Burned and how it can attain new Covers, including a demonstration of the question I asked here.
This is all spoilers for the story, of course.
Charlotte gives up her job at Starbucks and her ex-girlfriend Robin. “I hope you decide to
be a dude in your new life. It’s really going to confuse Robin and all of her shitty friends if
she has an ex-boyfriend all of a sudden, but it’ll serve her right.”
“I live with my two cats in Mr. and Mrs. Caruthers’ basement apartment,” he says, “and I
work in the coffee shop on Grand and 15th. Everyone knows me at the Silver Spurs, where
I have a beer and watch baseball at least two evenings a week. I once dated a lesbian named
Robin Small. My name is Abraham, but you can all call me Abe. My friends call me Abe.”
He opens his eyes and smiled at Cole. “And I have the bizarre habit of leaping into Lake Erie
on the coldest day of the year. Yes...this will do. It’s a bit scattered, but it will definitely do.”
Cole smiles, Charlotte starts laughing, and Alex, finally, lets himself slump down to the
I think it's worth noting that for Robin, there is probably no "all of a sudden", and it'll probably have been written off as a "phase", or something. This is never clarified in the story.