The ranges are on the same worksheet.

Right now, if NamesContatenated changes, NamesValues does not change at
all.

Note that I've pasted special--values (names) into the NamesValues
column/range, as this is what the sheet would look like if the code did
work.

The code is:

If Not Application.Intersect(Target, Range("NamesContatenated")) Is
Nothing Then
Application.EnableEvents = False
Range("NamesContatenated").Copy Destination:=Range("NamesValues")
Application.EnableEvents = True
End If

Also note that "NamesContatenated" is a calculated column based on
columns A and B, LastName and Firstname. NamesContatenated contains a
simple formula that combines LastName and FirstName and inserts a comma
in between.

So, NamesContatenated only changes when a Firstname or Lastname is
changed. If a firstname or lastname remains the same on worksheet
change, NamesContatenated, and subsequently, NamesValues, should also
remain the same.