Here is a workabout to your question :
Create a column SUM after the last column and calculate the sum of each row. lets say column V of your datasheet
then use the following array formula to filter the names whose sum is >=1
lets say you put this formula in X1 and drag and fill down until the last row.
=IFERROR(INDEX($A$2:$V$31;SMALL(IF($V$2:$V$31>=1;ROW($V$2:$V$31));ROW(1:1))-1;1);"")
this is an array formula, so press ctrl+shift+enter to calculate the formula
then in Z1 create your dropdown list based on the filtered names in column X.
please replace the 31 with 201 because you will have 200 rows plus one row of headings, if it is the case. I used 30 items in my example sheet.
tell me if it works.
***UPDATED***
sorry there was a mistake in the formula, it is now corrected. Here is the corrected formula. It now works fine. I also changed the download link.