I bloated up hippo's test Frame with the Solutions suggested so far and added some more test cases. They all do OK as far as specified and differ in the "unspecified by OP" cases:

#!/usr/bin/env perl
use 5.011;    # implies strict + feature 'say'
use warnings;

use Test::More;

my %names = (

    #           Test data
    #   input              expected output
    'BULLOCK JOE A'     => 'JOE',
    'SMITH, A DOE'      => 'DOE',
    'BULLOCK MICHAEL A' => 'MICHAEL',

    # not specified by OP:
    'SMITH ADAM'       => 'ADAM',
    'POCAHONTAS'       => 'POCAHONTAS',
    'TRAPPER JOHN M D' => 'JOHN',
);

my %approaches = (

    'hippo' => sub {
        my $fullname = shift;
        my ( $sname, $fname ) = $fullname =~ /([A-Z]{3,})/g;
        return $fname || $sname; # updated as per [id://1156306]
    },

    'Maresia' => sub {
        my $string = shift;
        if ( $string =~ /(\w{3,})$/ ) {
            return $1;
        }
        elsif ( $string =~ /(\w+)\s(\w{1,2})$/ ) {
            return $1;
        }
    },

    'kcott' => sub {
        shift =~ /^[^, ]+(?:,\s+\w+|)\s+(\w+)/;
        return $1;
    },
);

plan tests => scalar keys %approaches;
for my $who ( keys %approaches ) {
    print "\nRunning tests for $who:\n\n";
    subtest(
        $who,
        sub {
            plan tests => scalar keys %names;
            my $get_forename = $approaches{$who};
            for my $fullname ( keys %names ) {
                my $fname = $get_forename->($fullname);
                no warnings 'uninitialized';
                is( $fname, $names{$fullname},
                    "wanting forename '$names{$fullname}'  from '$full
+name'" );
            }
        }
    );
    print "\n";
}
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