It's common for people to not give SSN, but they don't need it. A name and date of birth is enough to match you to existing records the overwhelming majority of

It's common for people to not give SSN, but they don't need it. A name and date of birth is enough to match you to existing records the overwhelming majority of the time. Phone, address, insurance, and so forth, resolves the majority of what remains. Usually the only time they'll fail to ID you is when you show up to the front desk with no identification and lie about your personal details, which I don't particularly recommend doing.