I really don't see it that way. As far as I'm concerned, your identity is whatever you make it. I like to think it's malleable, rather than something simply thrust upon you at birth.
When you left Islam, you didn't lose a part of your identity - you simply changed it in order to represent yourself more accurately. A name change would have the same effect.
I can understand why most people would be uneasy about changing their name - it's due to
loss aversion: people don't like to give up what they already own. For those bold enough to overcome this inertia, a new name is like the start of a new legacy. All the different surnames had to originate somewhere, right? Rather than viewing it as a loss, we could consider ourselves pioneers trying to start afresh.
Just a thought.And a good one, thanks.
My social psychology teacher changed her name for personal reasons later in life too, and recently I have been more than toying with the idea of changing mine and my childrens, all together. Not only am I always asked if I am a muslim, but so are my children, and although they feel no confusion to explain that they are moroccan but not muslim, one day this could change.
When it comes to the ex muslim identity/label, that doesn;t bother me. For awhile I was extremely proud to carry that label and that torch to where it needed to go.
Of the 4 muslim women in my college, all of them know I am an ex muslim. How could they not when I handed in an essay on "has the quran changed over time" and I gleefully twiddled my thumbs as they went in a rage?

Am I hated by them for this label? fuck yeah I am, but I don;t care. Thanks to identifying myself as an exmuslim, the apostasy issue was something they were forced to deal with, and debate in a psychology lesson, and get thorougly trounced by the class. Not only that, but many people have come up to me to ask about this forum, the work we do, and to tell me about someone they know, who could do with the support.
This means that there is a use in my label, it helps other people and as long as it helps other people then I am proud to hold on to the label.
Sometimes it takes some people, being willing to stand there with a label that many others detest, in order to remove the stigma from that label.