My personal recovery from addiction is not dependent on whether other women who are new to recovery or have been in recovery for a long time identify themselves as "alcoholics" or "addicts." I really don't care if a woman ever claims those labels, and it annoys me that some members of some recovery fellowships pressure others to identify in those ways. It's not a requirement of any Twelve Step program.
Now, I do happen to refer to myself as an addict when I attend a certain recovery meeting. It's just no big deal to me, and I believe that there is a certain power to saying, "My name is Dawn, and I'm an addict," because I am modeling that it's just a word, and there's no emotional charge for me when I say it.
It's not my identity (although it was once), and I don't ever refer to myself as an addict outside of meetings. I don't need to.
You don't have to identify yourself in any particular way inside or outside of any meetings or anywhere else in recovery. And if someone tries to pressure you to, send them to me.
How we identify or introduce ourselves in recovery is up to us.