You'll need at least a 20% DP to purchase the next primary, and probably a signed lease proving rental income.

There really aren't any agents that do just leasing for people of residential homes 

that we’ve learned in our 24 years, managing almost 700 doors across the Metro Detroit area, including almost 100 S8 leases.

If you want it to be a business name, then I recommend you set up an LLC, transfer ownership to the LLC, and then change your leases to match the new owner name.What is your reasoning?

I've never come across such a vague lease agreement.

When I want to rent out this house, I am thinking of leasing it to an LLC which will have both me and my wife as members and that LLC will be leasing it out to the tenants.

My first did well based on selecting an area that we frequent.

I have a tenant on a month to month lease. 

Just add the Tenant's Rights and Responsiblities to the end of your lease and have them sign both at the same time.

As a new landlord, familiarize yourself with tenant laws and have a solid lease and screening process in place to protect yourself.Be prepared for maintenance expenses by setting aside funds, and if managing the property feels overwhelming, consider hiring a property manager to handle day-to-day tasks.