URGENT NEED HELP - Cox is not changing my account name from "Quick Connect"

I have spent nearly 5 hours straight on the phone with cox customer services reps trying to adjust my name on my account which is showing up as "quick connect" rather than my legal name. The reps I speak with say my account is setup as a business when it is a residential, so then they transfer me from a residential rep to a business rep, and the business rep tells me they can not make any adjustments as the account is a residential. And it is just a non-stop back and forth.

I went to a physical store nearby as well, spent another 2 hours there and they called from their backend line and they are giving them the same exact responses. They even submitted multiple tickets, but no one is able to give me a solution even with the submitted tickets. 

I even told them to just cancel my account, and they keep saying no one is able to do it, which makes absolutely 0 sense. How can you not just turn my service off?

My first bill is due soon, and I do not think I am legally obligated to pay the bill as it is not under my name. And I have been doing everything I can to resolve this issue, and have spent more than 10 hours of my personal time trying to fix it.

At this point I am not sure what to do, And I refuse to pay the bill as it is not under my name. Cox can cancel my account if they choose to I have no issue with that, but I refuse to pay the bill until it is corrected to my legal name as the account holder. 

Any help with this would be appreciated, thank you