Do I need a trade name if I get a LLC?

I am buying a pizza business in Ohio that is already operating. We will say that the name of the business is Larry's. I am getting an LLC and the name will be FSPR LLC. I need to know if this means that I am operating under a trade name that is different from it's legal name? And if this is the case will I need to apply for a DBA (Doing business as). A little confused about this and I don't want to file unnecessary paper work. Thank you