I signed up StackExchange sites with my google account. And StackExchange gave me a username automatically, like some sort of a user code. Is this username changable? How can I change it?
Go to your profile. There will be a small link labeled "edit", click on it.
There you will be able to change the aspects of your profile, including your username.
When you're don editing scroll to the bottom of the page and click the black button labeled "Save and Copy Profile to all Stack Exchange Accounts"
Note that the number on your username is your ID number and will always be. This is used to keep track of you across the network even if you change your display name.
Go to your page (under the username at the top), to the edit tab. There you can edit your account settings (including display name). But you'll be user63871 forever ;-)