I live in New York City. I invited my girlfriend to come and stay with me for 1 or 2 months because her living situation was precarious. It's now been 4 months. After repeated requests from me that she move out, we have broken up, and she still won't go. She has created a toxic environment here and has a temper that has frayed my nerves to the breaking point. She works, doesn't pay rent (never has) or any utilities (never has) and it is only my name on the lease. She receives mail here, but that's the only claim she has to the address.

Do I have to give her an official eviction notice, or can I just give her the boot? What are my legal rights here?

She gets mail there, therefore she has resident status. As a resident you need to treat her like a paying tenant.

Give her a written notice to vacate within 30 days or you will be forced to file for an eviction order. If she doesn't vacate then go to court for the eviction order.

You have rights, but so does she. And, as a resident, she has the right to not just be put out on the street.