You can't change your Skype name without making a new account.
You can change your display/full name without creating a new account:
You can change your display name without creating a new account. This
is the name that you see when you’re on Skype, and is displayed in
your friends’ contact lists, when you call someone on Skype, and in
the message area when you have an IM conversation*. To change your
1. Sign in to Skype.
2. In the menu bar, click Skype > Profile > Edit Your Profile….
3. At the top of the Profile tab, next to Full name, click your name. An edit box is displayed.
4. Type the display name you want to use and click the tick icon. Your name is changed.
Check out the Skype FAQ entitled "Can I change my Skype Name?" for more info.
If you do make a new user name, I don't believe there's a way to export/migrate the contacts. To move contacts you can probably log in as the old account on one computer, and the new account on another computer and then send your contacts from your old account to the new one. I'm pretty sure the contacts will have to approve being contacted by the new account, so you may want to warn them about the switch beforehand. :)
Perhaps check out "Can I transfer Skype Credit or Online Numbers to another Skype account?", from the same Skype FAQ.