Try this. Open both workbooks, then select a sheet without the names and in a cell type in a name. Then look to record a macro to use a Countif formula and you can switch to the other workbook to select the column and then switch back to use the criteria of the cell and then stop recording when you change the name in the cell to another one and run the code it should work and then you just adapt it to your userform.
Here is the sample code I recorded to give me the result
'Recorded Countif from one workbook to another
ActiveCell.FormulaR1C1 = "=COUNTIF('[List Names.xlsx]Data List'!C1,RC[-1])"