You could construct the filename at the moment you build the query, and pass it as a second argument to dumpResultsToFile():

my @tables = qw*TADA*;
dumpResultsToFile ( <<"    END_SQL", join('.', @tables) );
    SELECT $tables[0].fileName, $tables[0].labelName
    FROM   $tables[0]
    END_SQL

sub dumpResultsToFile {
    my ( $query, $filename ) = @_;
    ...
    open my $fh, '>', "$filename.txt" or die
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If you want a filename depending on tables, get the table names from their origin, i.e. where that information enters your program. Asking that information from some other module deep in the processing chain looks wrong to me, since you have it handy in the first place.