The thing I've mainly used named captures for so far is named access to the capture groups via %+. This can be very useful e.g. in cases like long regexes and/or if you've got one qr// regex inside another qr// regex inside another... keeping track of numbered capture groups quickly becomes impossible.

my $one = qr{      one (?<one> \d+ ) }xi;
my $two = qr{ $one two (?<two> \d+ ) }xi;
"One9Two8Three7"
    =~ m{ $two three (?<three> \d+ ) }xi;

use Data::Dump;
dd \%+;
__END__
{
  # tied Tie::Hash::NamedCapture
  one   => 9,
  three => 7,
  two   => 8,
}
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One bigger example that comes to my mind is this one: if you happen to have a 4th edition Camel (not sure if it's in the earlier ones), have a look at Chapter 5, Section "Fancy Patterns", subsection "Grammatical Patterns". You can basically build entire grammars out of them, for example using (?&NAME) you can recurse to a named subpatten (perlre; Update: a shorter example can be found under the documentation of (DEFINE)). Whether you want to build a full grammar using Perl's regex engine instead of one of the many well-established modules is of course another question :-)

Update 2: It seems I misread the question "What is the prevalent name for this feature" as "What is the prevalent use for this feature".

Update: Used /x and brackets to make the regexes more readable, eliminating a typo in the process. Changed the order of the paragraphs. Updated wording a little bit.