I've been divorced for around 7 years now, but I definitely feel more "single" than "divorced". I don't feel that divorce is a chief characteristic of mine, or of my life. It's more of an event that came and went than it is an ongoing state of being. I was divorced (in the past), hence I am single (now).
I remember posting a question about the absence of "Divorced" as a relationship-status selection here awhile back, and subsequently settling on "Single", because the other option, "Private", isn't really very descriptive (may as well keep it truly private by not having anything listed there at all, in that case).
I had the impression that "Divorced" was never provided as one of the relationship-status selections because it's considered 'scandalous' within churchdom, a failure of sorts, so maybe the rationale is "it's a bad thing so don't advertise it... keep such a shameful thing 'Private'", etc.
In my case, though, I don't see my divorce as necessarily a failure or an act of rebellion against God, but actually closer to an act of repentance, so feelings of shame don't really factor into it for me.