The advice you've been given above is far too severe in many cases. You've owned the building for four days and already talking about evicting a tenant for adding an unwarranted occupant? The first things you need to ask yourself are the following:
- How much due diligence did you do with the tenants in advance, prior to closing to establish a rapport with them and to go over what the new procedures will be?
- Per others above, what does the lease allow and how long is that lease good for?
- Is this really a big deal? If it's a one-bedroom you may have fire hazard remedies and code violations you could cite, but if it's a two-bedroom and there is room, is it a big deal if the tenants are good tenants who pay on time?
- What are you so worried about? In the rental game over your career, you will have 50% of tenants have an overstay guest or quasi-roommate that isn't on the lease. Is this against the lease, yes. But what if the person got kicked out of her house and needed a place to stay? What if they were escaping an abusive relationship? Before you start drawing up eviction paperwork, find out what the deal is.
Most errant new relationships between landlord-tenant start on the wrong foot because the new landlord didn't take the time to build a relationship before becoming the owner of the building. All tenants, when a duplex gets sold, think they are getting kicked out. Don't be so quick to push legal remedies as a landlord without more evidence. A bad tenant can ruin your unit so taking a first step to legalize the process on them won't win them over.