I'm assuming your anchor format is fairly rigid. If it's not, you will need a more complicated regex.

use strict;
use warnings;

while (<DATA>) {
    @_ = (); push @_, $1 while s/(<a name=".*?">)//i;
    $_ = join '', @_, $_;
    print;
}

__DATA__
This is an anchor <a name="_Toc00123998">and these are another <a name
+="_Toc00123999"><a name="_Toc00124000">couple.
This more anchors <a name="_Toc00123998">and more anchors <a name="_To
+c00124000">.
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