They can't "open an account in your name," per se, but if they legally own the debt they are free to invite you to repay it as if it's a line of credit and to charge interest consistent with your underlying contract (the one you signed with the hospital) and state law. I'm not sure why they would characterize it as a line of credit, though, as it seems unlikely that they are going to let you make additional charges to the account - and if they do they're subjecting themselves to disclosure laws and other regulations of the extension of credit.

