Identity theft and ISP – Information Security Stack Exchange

I have had multiple accounts open on my behalf. When I spoke to one of the account holders, this one stated that the order had been placed by my ISP. No one at my house could have opened this account. It is possible that a neighbor uses my ISP to open an account when he has my personal information. Also, is it possible that the fraud detection service of the online store where an account was opened in my name could easily tell me that the order came from my ISP?