Should I be worried-Co has diff SS#; same name?

I get my first utility bill - we signed up to get only emails no paper.

So we needed a copy of our bill for various stuff to prove we live where we say we do. I try to get access online, but my last 4 SS# isn't working with my account number so I call the utility company.

They look me up. They have my name, account number, but a different social security. But this lady tells me that can't be - if they don't match in the system, then it wouldn't work.

Now how the heck did that happen? I know there could be some one else with my name in the world, but what are the chances they could match up my social?