Assuming that your wife has, at some stage, received some pay from her employer, check what it says on the pay slip to see whether the employer is named as Stuffem Hall Care Home or Mrs E. Scrooge. Alternatively, if your wife was paid by cheque, what was the name of the account holder on the cheque? (If she was paid by transferring money directly into her bank account, look at the statement to see the name of the person/company making the payment).
If, at any point, there's an indication that the care home is a limited company, you should name the company on the paperwork. Otherwise, it shouldn't matter whether you name the care home or the proprietor, because their funds aren't legally separate. (If in doubt, use the name of the care home).
To check whether a company is 'limited', enter its trading name in the search facility here:
http://wck2.companieshouse.gov.uk/faea6524200d c9b91493e37261d658da/wcframe?name=accessCompan yInfo
Chris