Array formulate with multiple criteria without duplicates

Hi - I am attempting to pull a list of names from column A, based on whether they fit multiple criteria (the criteria is whether there is any text in column B OR column C).

I am struggling with the OR function, and even when I get close, I am still pulling duplicates (because there is text in column B and column C).

Here's what I think the formula should be (but obviously it isn't working -- instead this just pulls the full list without any filter)
=IFERROR(INDEX($A$3:$A:200,SMALL(IF(OR($B$3:$B$200<>"",$C$3:$C$200<>""),ROW($A$3:$A$200)),ROW(1:1))-2,1)"")

I've been reading through threads and piecing this together, so there may certainly be an easier way to do this. Any help is very appreciated!

Thanks

The former worked perfect!! Thanks so much