I presume your problem is that you have the names stored disassembled in an array. So reassemble the names using a character that won't occur in the name text as a part separator, perform the fix up, then disassemble the string again:

use strict;
use warnings;

my $match = join '|', 'Von', 'De La', 'De', 'La';
my @names = map {chomp; [split]} split "\n", <<NAMES;
Daniel R Von Vanderschmidt
Daniel Von Vanderschmidt
Daniel De La Silvia
Daniel De Silvia
Daniel La Silvia
NAMES

for my $name (@names) {
    my $nameStr = join '~', @$name;
    
    $nameStr =~ s/~($match)~/~$1 /g;
    $name = [split '~', $nameStr];
}

print join ('|', @$_), "\n" for @names;
[download]

Prints:

Daniel|R|Von Vanderschmidt
Daniel|Von Vanderschmidt
Daniel|De La Silvia
Daniel|De Silvia
Daniel|La Silvia
[download]