[regex] shell script. how to extract string using regular expressions

I am new to shell scripts. I want to send a http request using curl and then extract some string using regular expressions. For example, how can I extract a domain name from a http response? (The example is for learning purposes only)

#!/bin/bash
name=$(curl google.com | grep "www\..*com")
echo "domain name is"
echo $name

One way would be with sed. For example:

echo $name | sed -e 's?http://www\.??'

Normally the sed regular expressions are delimited by `/', but you can use '?' since you're searching for '/'. Here's another bash trick. @DigitalTrauma's answer reminded me that I ought to suggest it. It's similar:

echo ${name#http://www.}

(DigitalTrauma also gets credit for reminding me that the "http://" needs to be handled.)