As a latecomer to this thread, ++ to replies above as to syntax, applied to the logic of (some of?) OP's spec.

My problem is with the spec, "find a regular expression that finds 2 or 3 words on the same line (no matter what the order) and captures the values beside the matching words." which also includes this requirement: "to parse the file for lines containing "Fred Flintstone" "Barney Rubble" "Joe Rockhead"...."

#!/usr/bin/perl
use strict;
use warnings;
# 817539

my $pattern = qr/
    ^(\d)
    (?=  .* \bfred    \s+  (Flintstone)  )
    (?=  .* \bbarney  \s+  (Rubble)    )
    (?=  .* \bjoe     \s+  (Rockhead)  )
    /ix;

while ( my $line = <DATA> ) {
    chomp $line;
    if ( $line =~ /$pattern/ ) {
        my $lineno = $1;
        my $company = join '_', $2, $3, $4,  'inc';
        print "$lineno $company \n";
    } elsif ( $line =~ /(\d).*/) {        
        my $lineno = $1;
        print "$lineno, |$line|, does not match\n";
    }
}
__DATA__
1 bar Fred Flintstone Barney Rubble Joe Rockhead Alfred E Neuman
2 Joe Rockhead AE Neuman baz Fred Flintstone (does not contain name2)
3 Barney Rubble bat Fred Flintstone Joe Rockhead AE Neuman
4 Barney Rubble bat Joe Rockhead AE Neuman Fred Flintstone
5 Joe Jones bar Fred Flintstone Barney Rubble Alfred E Neuman(does not
+ contain Name3)
6 Barney Jones Barney Rubble Joe Rockhead Fred Smith  (does not contai
+n Name1 OR Name2)
7 Barney Rubble Fred Flintstone Joe Rockhead
8 Joe Rockhead Fred Flintstone Barney Rubble
9 Joe Rockhead Alfred Flintstone Barney Rubble (has Alfred sted Fred)
0 Joe Rockhead Fred Smith Barney Rubble (has Smith sted Flintstone)
[download]

Output:

1 Flintstone_Rubble_Rockhead_inc
2, |2 Joe Rockhead AE Neuman baz Fred Flintstone (does not contain nam
+e2)|, does not match
3 Flintstone_Rubble_Rockhead_inc
4 Flintstone_Rubble_Rockhead_inc
5, |5 Joe Jones bar Fred Flintstone Barney Rubble Alfred E Neuman(does
+ not contain Name3)|, does not match
6, |6 Barney Jones Barney Rubble Joe Rockhead Fred Smith  (does not co
+ntain Name1 OR Name2)|, does not match
7 Flintstone_Rubble_Rockhead_inc
8 Flintstone_Rubble_Rockhead_inc
9, |9 Joe Rockhead Alfred Flintstone Barney Rubble (has Alfred sted Fr
+ed)|, does not match
0, |0 Joe Rockhead Fred Smith Barney Rubble (has Smith sted Flintstone
+)|, does not match
[download]

In other words, is OP's spec, "2 or 3 words on the same line (no matter what the order)" sound and reasonable (esp. in light of the restriction to "Rubble,..." in another part of the question?

I raise the question because it appears that OP is trying to construct company names (say, for example, "Flintstone_Rubble_Rockhead_Inc") without regard to the fact that "Flintstone_Rubble_Rockhead_Inc" is not the same company as "Rubble_Flintstone_Rockhead_Inc".

BTW, Lain78's use of alternation addresses my question about the significance of the order of names but veers off the One_True_Way (True_One_Way ??) in failing to use strict; use warnings;.

Update: Fixed missing i tag in 2nd quote; added "requirement" for clarity -- both in 2nd para.

Update 2: OP's update in Re 4, "parsing settings from a config file" casts the problem very differently (assuming the inconsistent ordering in the config is inconsequential) but highlights a thought for any who consider posing a question with the real need obfuscated in a scenario unrelated to your real purpose: Don't; you may be wasting your time and that of the Monks who try to help.