use IO::Handle;

my ($fname1, $fname2) = qw(1.txt 2.txt);
open my $fh1, $fname1 or die $!;
open my $fh2, $fname2 or die $!;

while (1) {
    foreach my $fh ($fh1, $fh2) { 
        my $line = $fh->getline();
        if (defined $line) {
            my $fname = $fh == $fh1 ? $fname1 : $fname2;
            print "$fname: $line\n"
        } else {
            sleep 1;  # be nice
        }
    }
}