I understand that if I rent this ADU out, then I can have a tax write off on the mortgage payment and insurance payment for the the ADU's sqft portion.

Find yourself a good team who builds ADU's has a project management team and of course has all the licenses and insurances to protect your property.Quote from @Michael Adamo: Hi BP Community,I’m exploring adding one or two ADUs to a property I own in the Miracle Mile area, near 3rd Street and La Brea in Los Angeles.

Is your DSCR ratio greater than 1-meaning are you cash flowing (according to the lender's criteria of mortgage, property taxes and insurance (and HOA) if applicable).

Hopefully you have the correct insurance in place etc.Hope this helps

You can try to go after their renters insurance, but since you don't have proof, you're probably not going to get anywhere.

There is title insurance issued at the time of purchase, so we don't want to invalidate that.

@Benoy Varghese When I take over a property I send a letter to the existing tenants introducing myself and telling them where to send rent and provide the necessary information regarding my policy for dealing with maintenance issues.

Insurance, bank accounts, credit cards, etc.You are probably making your life more complicated and expensive than it needs to be.

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? 

I own a lot more than 2 homes and all these years later still have never bothered with LLCs - I just keep really good insurance.