Where do you live? Divorce is so common among my coworkers and really among everyone I know that no one bats an eye when it happens. I work in a place with about 30 people and one is in the fighting-about-alimony stage and another just filed for divorce. We are very supportive when it happens even we know the ex socially.
I can see not wanting to discuss it when you are just starting a new job and there is no reason you have to. If you're asked you can say you're married, because you are. By the time your divorce is final you might feel more at ease talking about it.
Divorce is a wrenching thing to go through even when you are the one who wanted it. I was in that place about 15 years ago. Horrible. But it gets better.