IF Function For Last Occurring Unique Cases?

I have an excel file that lists individuals who came into the clinic on a given day. I am interested in figuring out the amount of unique individuals in a given month/overall. As this is a working datasheet, I would like a formula that would automatically update this information for me. Here is an example of the file that I am working with: unique case example.xlsx

Specifically, I want an IF function that could place an 'x' in column E depending on if the name in column C is a unique instance. But if the name appears several times in the list, I would also like this function to place an 'x' in column E next to the last occurring unique instance. For example, the name 'Hanna D' occurs 3 times in the spreadsheet I have attached, but I want the 'x' to be next to the most recent incident, when she was screened, as opposed to when she was not contacted (missed/doc forgot).

I am not sure if you can even define a unique case in the IF function, let alone the last occurring unique case.

I am not interested in conditional formatting (highlighting duplicate cases and then placing an 'x' next to the most recent highlighted case) because my spreadsheet has 300+ individuals and it is very time consuming to manually move the 'x' when the same individual appears at a later time.