Your pattern with less leaning toothpicks (removed needless escapes of "<" and ">", and used an alternate delimiter to avoid escaping "/"):

s{(<value>|\G)(.+?)\|(.+?)\|(.*?)(?=</value>)}
 {$1$2</value><name>$3</name><value>$4}sg;
[download]

What it should match for each pass of /g:

Pass 1: <name>(test)</name><value>(431)|
Pass 2: (alpha)|(123)|
Pass 3: (bravo)|(542)|
Pass 4: (charlie)|(412)</value>
[download]

What it does match for each pass of /g:

Pass 1: <value>(431)|(alpha|123|bravo|542|charlie|412)
[download]

Fix:

s{(?:<name>(.*?)</name><value>|\G([^|]*?)\|)([^|]*?)(?:\||</value>)}{
   "<name>" . (defined($1)?$1:$2) . "</name><value>$3</value>"
}seg;
[download]

A much more robust fix:

s{<name>(.*?)</name><value>(.*?)</value>}{
   my $s = "|$1|$2";
   $s =~ s{\|([^|]*)\|([^|]*)}{<name>$1</name><value>$2</value>}sg;
   $s
}seg;
[download]

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