I am struggling to develop one of those "copy down" functions that can
produce a set of values. In this simplified example, the formula needs to
tell me the name from column A if there is a value in the remaining array
(B1:D5).

Dave 1 2 3
Bob 1
Sarah 3
George 2
Sally 1

So the first instance of the formula would produce "Dave", the second would
produce "Bob", the third ""George", the fourth is "Dave" again, followed by
"Sarah", etc. Yes, I need it to read the array down the first column before
it moves on to the next column.

For what it's worth, here's what is not working for me:
=INDEX($B$15:$B$68,SMALL(IF($C$15:$Z$68<"",ROW($C $15:$N$68)-14),ROWS($B$70:H70))).
It's an INDEX function using the SMALL function to produce sequential values
and the IF function to identify all the places where the array is populated.
It's entered as an array function, of course.

Any ideas? TIA