What have you tried so far?

How did you implement the search?

#!/usr/bin/perl -l
use strict;
use warnings;

my @names = (
    'Jones',
    'Jones Jr',
    'Jones Sr',
    'Jones abc',
    'Jones ',
);

# may be filled from form value
my $search = 'Jones';

my @regex = (
    # simple
    qr{\Q$search\E},
    # anchored
    qr{^\Q$search\E$},
    # anchored and extended
    qr{^\Q$search\E(?:\s+\w+)?$},
);

for my $regex ( @regex ) {

    print "\n\n$regex";
    for my $name ( @names ) {
        print "matched: $name"    if $name =~ $regex;
    }
}

__END__
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Beware; there's still room for improvement. Try that example and examine the results.