Open Question: I have a question regarding my business ( DBA's )?

I currently have a business entity, an s-corp llc out of the state of delaware, I am starting another business under a DBA, It is my understanding that I do not need a new tax id for the DBA, but I just want to make sure that the ownership is still under my parent company, futhermore I run my business in the state of Ohio and like I mentioned I set up my corp in the state of Delaware for legal reasons, so would that present any problems, thank you for your help.