how do I switch data cellular plans on an iPad?

I used to have a Verizon data cellular plan but I cancelled my Verizon account altogether (personal email, etc).

But my iPad still defaults to show "Verizon" in the upper left screen. At home I have wireless with another company,

which allows me to use an iPad from home. How do I buy a cellular data plan with AT&T? When I go into 'Cellular Data Account,'

the screen still defaults to Verizon and says I have an invalid SIM card. This is BS - we don't live in an information monopoly -

how do I choose another cellular plan and erase this default? Thanks for any help!