I've been mulling over this since I read it as a submission for the DUFC. Identity, and labels for it, is something I've always found intriguing. MsElouise provided a different way of thinking about it for me. She concluded that claiming a label can help you feel that you belong and give you a voice, but it can also be a trap. One reason it can be a trap is that some people may hold quite different ideas about the identity you claim than you hold yourself. When "some people" is a large chunk, or even a majority, of society, the identity ends up a constant source of mis-identification and outright prejudice. This can be a damn good reason to reject a label, although it sucks to have to acquiesce to prejudice and ignorance and for some identities (race, gender & sexual identity for eg) is the basis of activism.
In thinking about the reasons why people might reject an identity, or at least the label for it, I think she's nailed one of the reasons. However, I think there's another one that relates to fear of rejection and impostor syndrome. In part, I don't say "I am a feminist" (while having entirely feminist ideology) because I worry about being trapped in what other people think a feminist is. This is the aspect I've focussed on in the past. I've never been happy with all the connotations of any label, so I've rejected all of them. But another part is that I fear being rejected by feminists as not a good enough feminist. I wouldn't call myself bisexual because "real" bisexual people would laugh at my married-to-a-man arse. If I don't claim the identity, other people who share it can't reject me.
Any given label I reject may have elements of both reasons, or be based entirely on one of them. I think there are probably more reasons too. My disinterest in my surname probably has more to do with historical accident and perversity than anything else.
Also worth noting is that some labels I don't have the right to reject - the ones that are given to me by society and luck and provide me with a head start over people who don't share them. White, middle class, educated, cis, perceived as hetero. Those labels I need to remain aware of until such time as other labels are afforded the same advantages and opportunities. Only then will it truly be meaningful for people to have a choice as to whether they want to embrace those socially loaded identities and labels or not.