open ($handle, 'surnames.html');
while (<$handle>) {
    $hash{$1} = () if m/^<\w+?><B>(\w+?)<\/B>/;
}
close ($handle);
print '"' . join ("\",\n\"", sort keys %hash) . '"';
[download]

To expand a little on TedPride's terse code segment, he is suggesting you open the page in your browser, save it as "surnames.html" in the same directory as a script with his code, then run the script and feed "surnames.html" to it through STDIN (like perl script.pl < surnames.html).
Also note that the bold tags in the script are lower-case, so you probably want to make your match case-insensitive by adding the /i modifier to your regex. Finally, if all you're interested in is the "Mac"s (as your original code fragment suggests), you might want to update the regular expression a little:

open ($handle, 'surnames.html');
while (<$handle>) {
    $hash{$1} = () if m/^<\w+?><B>(Mac\w+?)<\/B>/i;
}
close ($handle);
print '"' . join ("\",\n\"", sort keys %hash) . '"';
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[id://TedPride]'s code has taken advantage of the fact that all the surnames are between <b> tags. The regular expression matches any text that starts with a general tag (<\w+?>, like "<br>"), is then followed by a bold tag (<B>) and a name starting with "Mac" and one or more following characters ((Mac\w+?)). The parentheses "capture" the matched text to the special variable $1.
Updated after [id://Anonymous Monk]'s post below.

then run the script and feed "surnames.html" to it through STDIN (like perl script.pl < surnames.html)

That's not what he's suggesting at all. He's using open to open surnames.html.

my @a =
(
    "MacAchallies",
    "McAchallies",
    "MacAchounich",
    "McAchounich",
    "MacAdam",
    "McAdam",
    "MacAdie",
    "McAdie",
    "MacAindra",
);

for ( @a )
{
    print "$1\n" if /^Ma?c(.+)/
}
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my @names = qw "MacAchallies McAchallies MacAchounich McAchounich MacA
+dam McAdam MacAdie McAdie MacAindra";

for(@names){
   $_ =~ /M.?c*/ and print $'."\n";
}
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fauria:

Your regex, "/M.?c*/" will do fine at finding "Mac" or "Mc" and printing the REST of the name (rather than what the OP sought), and recall that c* matches ZERO OR MORE "c"s, meaning non-names, like Mccccc (ill-formatted roman numerals??) will match.

Also, as written, (without capturing parens) it prints:

Achallies
Achallies
Achounich
Achounich
Adam
Adam
Adie
Adie
Aindra

whereas (with slightly different use of quantifiers and a couple additional names as test cases), this appears to work as requested:

#!C:perl/bin

my @names = qw "M Mac McA Mcccccc MacAchallies McAchallies MacAchounic
+h McAchounich MacAdam McAdam MacAdie McAdie MacAindra";
 
for(@names){
   $_ =~ /(M.?c+.*)/ and print "$1\n";
}

=HEAD  output is:
Mac
McA
Mcccccc
MacAchallies
McAchallies
MacAchounich
McAchounich
MacAdam
McAdam
MacAdie
McAdie
MacAindra

=cut
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Noted also, that using $' (and friends) incurs a lot of overhead.
And, just because they're not here, use strict; use warnings.

my @a =
(
    "MacAchallies",
    "McAchallies",
    "MacAchounich",
    "McAchounich",
    "MacAdam",
    "McAdam",
    "MacAdie",
    "McAdie",
    "MacAindra",
);

print grep { s/^ma?c(.+)/$1\n/i } @a;
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