I would try getting a supervisor on the phone - tell them you would like to cancel if they don't follow through (which you can actually do since you just opened the account). At the very least they should give you some kind of discount.

It's a new account because of the new name for the billing, but the same phone number and start of contract date. Do you know if there is a way to make them true to their original word? I've been very disappointed with their customer service at this point and I'm thinking about jumping ships on cellphone companies because of it.

If they setup a new account with a new number, they can't keep an old unlimited plan. They shouldn't have told you otherwise.

I transferred my line being told I would have my grandfathered unlimited iPhone data with it. I had made it very clear I was more concerned with that than the cellphone number itself. After being reassured this I transferred the billing rights over and now have had to deal with endless headaches of them claiming they can't do this. I've been a customer for years, but I'm thinking about changing companies now.