Even without a lease or any agreement, you have the rights of a month to month tenant simply by virtue of making your residence in her home. That means she can not evict you withiut 30 days notice that the "tenancy" is terminating.
Renting a place together and signing the same lease is the most common way that two people become cotenants. But you and your partner can become cotenants in another way, too. If you have a place and your landlord approves of an additional occupant, your partner can sign your original lease and become a cotenant.
For guests staying for an extended period (such as several weeks), the tenant should inform the landlord of the situation. If a landlord tries to evict a tenant for having occupants in a rental unit, tenants can seek dispute resolution.
You are not required to tell you landlord nor can they inhibit the guest from entry. If they ask, you are required to say but nothing actually has to be done during your existing lease. I went through the same thing last year when my gf moved in for a few months, also a rent stabilized place.
In most cases, it is possible and easy to add someone to an existing lease if it's allowed by the landlord. However, the landlord will need to write a lease addendum or lease amendment to add new information to the lease that can protect all parties.