What you want is an owner-occupied two-to-four family policy. Carriers name it differently, and on the standard homeowners forms it's often a homeowners policy written for a two-family dwelling, sometimes with an endorsement noting the rental exposure. A landlord policy, which you'll hear called a dwelling fire or DP-3 policy, is built for a building where the owner doesn't live, and it usually carries thinner personal property and personal liability coverage than you'd want on the home you actually sleep in. That's why the agent wants to start over.
Three things to ask them to price. Rebuilding cost for the whole building, since you own both sides. Liability limits, because a tenant's guest tripping on your shared stairs is your exposure. Loss of rent coverage, sometimes called fair rental value, which pays the rent you'd have collected if the tenant's unit is unlivable after a covered loss. Your lender will require coverage at least equal to the loan amount and will want to be listed as mortgagee, so send them the declarations page before closing.
Your tenant's belongings aren't covered by your policy at all. Requiring renters insurance in the lease with a minimum liability amount is normal and cheap for them, often under $20 a month.
On licensing, renting units you own generally doesn't require a real estate license. Plenty of cities and some states do require a rental registration or a certificate of occupancy inspection per unit, with fees often in the $50 to $200 range, and some exempt owner-occupied two-unit buildings. Call your city's housing or code department and ask specifically about your address.
