All credit reporting bureaus index credit information by social security number and name. When a creditor requests or reports information, the credit reporting bureau uses a consumer's name and social security number to organize the information.
This is why consumers are generally advised not to give out social security numbers hastily. With an individual's social security number another can gain access to your credit report and use that information to commit fraud by using existing accounts to make purchases or, applying for new accounts. The information contained in the personal credit history is personal and not something you want anyone without permission to access.
The fact the files are indexed with social security numbers and names is also why errors occasionally occur and someone with the same name has their credit history "bleed" onto another.