Changing website address possible?

Probably can, but need to pay for and register another one?

Yes.

Also see:

http://codex.ww.wp.xz.cn/Changing_The_Site_URL

You have to buy a domain.
Setup DNS.
Update dns record of hosting.
When u update the dns, u can no longer access your site.
Login to phpmyadmin>click on your site’s database>click on wp_option table>Edit siteurl and home.