Countifs On Cells With Multiple Entries

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I'm using the Countifs formula to count the number of times a name in the Name column is entered based on criteria in another column.  The issue I'm having is when a cell in the Name column has multiple names.  It appears Countifs matches the entire cell to my criteria, not if my criteria is contained in each cell.  Is there a way to get a count of a name when it is listed with other names in a cell from the Name column I'm referencing?

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Let's say the names are in B2:B50 and the name you're trying to count is in D2.


=COUNTIFS(B2:B50, "*"&D2&"*")