foreach my $line (<DATA>) { #assuming you have a data source
    chomp $line;
    @lines = split /\\n/, $line, 4;
    foreach $l (@lines) {  # <--that's an L, not a one
        $l =~ s/^,//;
        @elems = split /,/, $l;
        print "$_ " for @elems; print "\n";
    }
}

__DATA__
name1,a1,b1,c1,\n,name2,a2,b2,c2\nname3,a3,b3,c3,\n,name4,a4,b4,c4
name5,a5,b5,c5,\n,name6,a6,b6,c6\nname7,a7,b7,c7,\n,name8,a8,b8,c8