Don’t leave it to chance market the unit and stick to your standards.  

They ask about staying long term, hoping the thought of all that money will entice you to interact with them and leave your defenses down. 

The tenant fails to pay their last month's rent and leaves the place needing new flooring and paint.

Should I still do some sort of addendum to the existing lease to have it in my name, or am I okay to leave until renewal in January?

If they paid full October rent, then I would wait and see because if they gave notice and leave mid month, I owe them prorated rent in return.

This creates two loan payments ($100,000 of equity and $300,000 on the new mortgage).Key NumbersHome Equity Loan Interest Rate: 6%Mortgage Interest Rate: 7%Rental Income: $3,000 per monthExpenses (management, taxes, insurance, maintenance): $800 per monthIncome and ExpensesMonthly Rental Income: $3,000Monthly Expenses: $800Monthly Mortgage Payment: $2,000ExplanationThe investor earns $3,000 in rent each month.They pay $2,000 on the investment property mortgage and $800 on other expenses.This leaves $200 profit each month or $2,400 per year.However, you have to pay $6,000 interest on the equity borrowed.This leaves you with an annual loss of $3,600.This example shows that while the rental property generates positive monthly income, the interest cost of borrowing the initial $100,000 results in an overall annual loss.

That leaves you with NV,WA and now TN. 

At this stage, you want to ensure that the property is cash-flow positive, meaning the rent covers expenses and leaves a profit.4.

Other answers might include the acronym CIA:  Credit Income and Assets but that leaves out the items Brandon mentions.   

I am not sure she is going to leave me alone.Would you pay a lawyer to write a letter to leave you alone or just do as you say and if she does file a small claims just deal with it then?