Change rental agreement to LLC name?

[Sorin T]

Hi, seasoned landlords, need some advice from you. I bought this property (TH) rehabbed it and rented it, all under my name. Naturally, the lease agreement carries my name as the landlord. Now, I read through a lot of material on this site and understood that it's better to have that under an LLC, to protect my private assets from any mishaps. I formed an LLC and plan to quit claim deed of that property from my name to the LLC. My question: do I need to redo/rewrite the lease agreement to reflect the LLC name? Or just be mindful and do the next agreement for the next tenant under the LLC name? Can the current tenant sue me for any reason (hope not) if the lease has my name on it but the property has been transfered into LLC?

Thanks for all the help, the wealth of information here is unrivaled anywhere else and seasoned investors are very helpful with newbies. AWESOME PLACE!