Texas · Renting the house changes the form
A landlord policy insures the building and lost rent after a covered peril. It does not insure the tenant’s furniture, ordinary wear, or flood. This page will not invent a vacancy period or a premium.
An HO-3 assumes you live there. A rented house needs a dwelling form. Loss of rent pays only when a covered peril, hail or fire for example, makes the unit unlivable. It does not pay because a tenant moved out. The tenant’s HO-4 covers their belongings and their liability, not your rebuild. Texas does not set a statewide renters dollar minimum. A lease can still require a liability limit. Naming you as an interested party gives you notice if they cancel. It does not insure the building.
The split: landlord versus homeowners, what moves the cost, and becoming a landlord. What you can ask the tenant to carry: renters limits. The lease is not the policy: tenant-landlord law. A house you use yourself is different: second homes. Flood is local: flood, including inland. The idea of the policy: what landlord insurance is for.