Why do I have 2 Wi-Fi Connection of the same name?

It has been more than a year since we last had internet, and a week ago we finally registered for a new one. The internet people set up the connection and had named the Wi-Fi connection "INTERNET" and the password is 123456, due to I was at school they didn't know what username and password to be set up. It's pretty obvious and I do not share my internet connection with anyone.

I yahoo-ed and google-ed everything and ask BUFFALOTECH, the brand of the Wi-Fi and router for help in resetting the whole password and name. I pressed the little pinhole button "RESET" and was asked to create a new router/connection. Formerly known as BUFFALO-5D32F8-1. When I've set the name and password and everything, I realise that my iPhone was connected to a Wi-Fi connection named BUFFALO-5D32F8, but my new Wi-Fi name and password is available as well. How can this happen?

I was wondering, how do I turn that unsecured connection off as it's sucking my internet connection away from me and other people are able to connect to it?

Sure it is yours and not someone else close by? Turn yours off and see if it disappears.
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Install techs are lazy and frequently setup routers the same for everyone. You may have a neighbor who had the same tech.

Restore your devices to its original set up. I think this may solve the problem

Just restart your router

and delete the Wi-Fi profile from your iphone