First of all, those anchors are broken. They are missing an open quote and need ether to be self closed or explicitly closed.

Second, it is a bad idea in general to try to parse HTML with regexes. HTML is not necessarily regular markup and can not be reliably parsed with a regular expression.

However, within those constraints, something like the following should do what you ask with either self closed or explicitly closed anchors.

use warnings;
use strict;

while (my $line = <DATA>){
    my @anchors = $line =~ m#<a name="[^>]+?(?:/>|></a>)#g;
    $line =~ s#<a name="[^>]+?(?:/>|></a>)##g;
    print @anchors,$line;
}

__DATA__
Self: This is an anchor <a name="_Toc00123998" />and these are another
+<a name="_Toc00123999" /><a name="_Toc00124000" /> couple.
Explicit: This is an anchor <a name="_Toc00123998">no cap</a>and these
+ are another<a name="_Toc00123999"></a><a name="_Toc00124000" /></a>c
+ouple.
[download]

Update: modified to not capture anchors with enclosed text.

Update2: Arggh. Try that one more time