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="_Toc00124000">.