..so that I can get the bare host name 'google.com'
um, google.com is not a hostname, it's a domain name.
Also, you start your example with 'www.google.com', and then you say you want 'google.com'
Is that correct, or was it a typo?
I'll assume you want to extract the Fully Qualified Domain Name
..appreciate some advice and whether split is the right function to use or not?
Although you could get what you want with split, I wouldn't consider it the best thing to use here. Especially if you're dealing with more complex URL's.
Personally, I'd use URI::Split
use URI::Split qw/uri_split/;
my $url = 'http://www.google.com';
my ($proto, $fqdn) = uri_split($url);
print "Protocol:$proto Domain:$fqdn\n";