I am contemplating suing my former landlord about some issues with my security deposit. According to the handy reference from the Tenant's Council, I need to know the correct names and addresses of the defendants, so that the court can legally grant a judgement. I gave the apartment complex's name and what I think is the name of their parent company (it shows up on their website), address, and phone number to the Secretary of State's Corporate Division to see if they could get me the legal name and representative.

Their response is: There is no corporate record listed for the captioned name as either a business corporation, limited partnership, limited liability company, nor assumed name.

So what's my next step in figuring out who to sue?

I would try Property Appraisers office for that county, and look it up.
Some have websites and you can look up by address.