Determine if item from one worksheet is in another, if not copy to new worksheet

Hi all, first post here.

Im a noob to VBA and excel macros in general. I have pretty good programming experience but havent touched vba or tried this yet. I have a work task I volunteered to complete on a short time frame and Im hoping to speed the process by using everyones collective knowledge here!

I have a spreadsheet that has patient information from a medical office. I have another list that has some patients that are not included in the first list. There are ~5000 patients in the smaller list, and it looks like im going to be coming up with ~1000 patients who are not in that list, which are the ones of interest. I want to find a way to copy the patients NOT in the smaller list into a new worksheet.

The names are the values of interest, so I am looking to choose a name value, search the workbook for its presence, and if its not there copy to a new sheet.

Mainly what I am interested in is the syntactical particulars of this, and how to go about this search in VBA as I dont have any experience here. Any pointers would be helpful!

P.S. I cant post the spreadsheets as they are private information and doing so would be a HIPPA violation.