My question involves landlord-tenant law in the State of: Suffolk County, New York

My sister has a year to year lease with her landlords.
There is someone renting a room from from my sister for $600/month.
There is no lease.
Mrs. Landlord knows about the roommate but Mr. Landlord doesn't. (Thought I'd throw that in there in case it's relevant)
My sister has asked the woman to move. She gave her 30 days, but not in writing (yet).

Can my sister legally evict her on her own or does it have to be done by the Landlord?

What about if they don't call the money "rent" and the money is just used for utilities? I read a long time ago that if the money is called "rent" it makes the receiver a "landlord" and the payer a "tenant" Does that affect who if they can be evicted and how?

thank you for any advice.