Since there's always more than one way to do it, you could consider operating on each part of the name befor doing the join:

sub fullname {
  my (@parts) = @_;
  
  for my $p (@parts) {
    $p = length($p) > 1 ? $p        : # not a single - don't change
         $p =~ /[a-z]/i ? $p . '.'  : # single letter - add a dot
         $p;                          # not a letter - don't change
  }  
  my $name = join(" ", @parts);
  return $name;
}
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Breaking it up like this might be preferable if the problem were more complex, because really long regex's can be difficult to maintain. For example, if you decided to add a dollar sign in front of single digits, you could just add this line (after the add a dot line):

$p =~ /\d/  ? '$' . $p     : # single digit - add a $
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This seems easier (to me) than rewriting the regex, and less likely to introduce subtle bugs due to differences in regex behavior.

Unless you're a regex master, I think it's best to keep them as simple as possible. And if you ARE a regex master, but have to work on a team where other people are NOT - then it's STILL best to keep them simple as possible!