Is this job a unit clerk? I want to visit patients in the hospital and see if they need anything, basically supporting them emotionally?

That would be a volunteer, chaplain, or case manager- although chaplains and case managers do a lot more than just visit patients.

The link you posted sounds like a volunteer position or part of a student community service program, not a paying job.

No that is not a unit clerk. That could be a case manager, a nurse, a volunteer, etc etc but its not a unit clerk.

That's handled by the patient's case manager, typically a RN. The unit clerk is a clerical position; handling phone calls, managing patient files, arranging for lab/radiology/etc. They have little contact with patients.

where i live, there's a social worker who does that, as well as the chaplain