That all depends on whether you're in on the identity group
In the end, identity groups are more of a consensus thing, as there has to be a general agreement whether you fit in or not. I just recently saw this movie called "the spook who sat by the door", it's about these inner city black people who start this militant group called the "freedom fighters". One of the people in the group is a white guy but refuses to be identified as white, and because of his loyalty to the people he spends time with, they never question it, they let him be a "real" black person. His ideas about who is don't faulter, and so nobody in the film tries to take that away from him! Things don't always work out that way though....
The anarchist identity is different from a lot of the identities you point to:
"socialist, conservative, woman, vegan, trans, poor, jewish, rebel, ...."
most of these categories (with the exception of "rebel" or "socialist") are more demarcated and accepted by general society, whereas nobody really has much of a clue as to what "an anarchist" is, or what it means. An individual identity is one that doesn't give a shit about what other people think, and in my opinion is therefore less useful. Overall, i don't find any identifier outside of a description of what one regularly does to be worth as much as a grain of salt. For example, "a doctor" or "a guitarist" gives me a lot more clues about what a person is like than "a poor" or "a conservative"
"do you think of yourself as an anarchist?"
meh, not very often. Around election season I do, it's nice to have that reminder of why i don't need to march to the voting booth. I'm an anarchist to the extent it describes my perspectives on politics. I also have used it in decision making to keep myself from getting stuck in forms of bondage, but for the most part i don't need to think of it like that. As stirner alluded to...if you don't use an idea then forget about it.
All this weirdness is why i try to keep a sense of humor about my screen names on line ("Nihilist" X-D), the more absurd and silly the better!