Trying to unlink accounts

Hi, I have one account that is tied to Internet service at my house. I also have an older account from when I tried to initially set up service that went inactive. I had to set up a new account and then link them to continue using the same name - at least this is what I was told by the agent that assisted me.

However, I don't care about being able to use the same name anymore and would just like the old account completely removed from my profile. I spoke to someone on the phone who was able to help unlink them, but when I tried to claim the newer account with new login details, it recognizes the phone number and email address from the older inactive account. I ended up logging back in since I don't have another phone number to use and it automatically linked them again, putting me back at square one.

Hopefully this makes sense, as it's a bit confusing to explain. Would anyone be able to help me with properly and permanently unlinking the old account so I can set up new login details?