If I keep the house in my name and use it as a rental, would I need to do anything other than notify the lender and adjust my homeowners insurance to reflect the house is a rental? 

Currently speaking with a local realtor about the STR zoning issues, insurance issues, and current/future market in Florida. 2025 should be a good time to look for a property there. 1.

For insurance, I’d recommend working with a local broker to explore the best rates.

Buy a single-family home, and someone tries to sell you on property management or insurance.

Your insurance is going to be highly variable and I wouldn't use what an agent or the seller tells you as the cost of dwelling policies have increased substantially over the past few years due to rising new construction costs. 

If you are struggling to make the numbers work, then it is likely not a deal to pursue.Our biggest challenge in the New Orleans area is the cost of insurance.

Well if Proper won't insure it, many others won't as well.

Is that just the mortgage or are you counting in insurance and taxes?

Here it would be 25% down ($275k)A balance of $825k at 7% (or higher) $5,490/mo, figure $250/mo insurance, $500/mo property taxes $6,250/mo. 

Now if you didn't refinance rented that unit out before living in it for a year and changed your insurance policy to a commercial one, that could be problematic (just to give an example).