Try Auto Filter or Advanced Filter are the best way to do. If you preferred
the formula then
try this:
"Name" is a define name range
"PSTFS" is a define name range

=IF(ISERR(SMALL(IF(PSTFS=0,ROW(INDIRECT("1:"&ROWS( Name)))),ROWS($1:1))),"",INDEX(Name,SMALL(IF(PSTFS =0,ROW(INDIRECT("1:"&ROWS(Name)))),ROWS($1:1))))

ctrl+shift+enter, not just enter
copy down

or this:
=IF(COUNTIF(PSTFS,0)=ROWS($1:1),INDEX(Name,SMALL( IF(PSTFS=0,ROW(Name)-MIN(ROW(Name))+1,ROWS($1:1)),ROWS($1:1))),"")

ctrl+shift+enter, not just enter
copy down

"Diamonds_Mine" wrote:

Below is a sample list; I need to extract or highlight names in Column A that
have a zero value in column B, but if the name in Column A is listed multiple
times and the value in column B is greater than zero, it should not be
extracted or highlighted. So for the list below the result should be User 4
and User 5. Thank you.

Column A Column B
Name PST Folder Size
User 1 0
User 2 15
User 3 18
User 1 22
User 4 0
User 5 0