Yes, the company can change its name. But how you handle it depends on why. Was it bought by another company? Just change its name? Incorporate or become an LLC? Any of those things could result in a change of name. Usually, the new entity assumes liabilty for the old entity and you should conduct some discovery to uncover what happened. Then you will know what to do. You may be able to get a stipulation that the newly named entity is the entity liable under your law suit.
The answer to the question "Can a company change its name?" the answer is yes. Do you have to "start all over again"? I would think, no. I'd check with a lawyer admitted in Louisiana (I'm only admitted in CA), but at least under CA law, you can amend the complaint to properly name the defendant, though in your state it may require Court approval. It is important to amend the complaint, however, because if you prevail and get a judgment against that defendant, you will want to make sure that you have the right company, or your judgment may not be worth much if the judgment is in the name of the former company only.