I work for home health care and I work 12 hour days, they single staff me with 2 clients, but only pay me for one. Should I be paid for both?

tell whoever is responsible to send another caregiver for the 2nd person
If they do not, ask for a single client workload.
If they do not, quit.

Are you working in a NH being paid hourly or for an agency that is sending you to a home where two people need care and you are getting paid for one. Interesting question.

This probably should be answered by BurntCaregiver since she owns a Caregiving business.

Did you sign an employment contract? If so, read it. Did they give you any other employment handbook or job description? If so, read it. Check the labor laws that pertain for NHs or facilities for your state.