Changing the Magento Admin URL is not simple and if done wrong can kill your site so check on your DEV site first.

Note: Do NOT use the web interface in the Magento Admin Panel to change the admin URL, as this is known to cause severe problems. (at time of writing)

Change Admin URL

• The admin URL is set in the local.xml file
  • default 0 admin/url/use_custom
  • default 0 admin/url/custom
• And under System->Configuration->Admin->Admin Base URL I have set 'Use custom admin URL set to “Yes”  - Check this
• Clear the cache

Links

• How to change the Magento Admin URL / Path
• Magento admin URL change
• Change Admin URL Manually
• Magento. How to change admin panel URL - Template Monster Help

And this forum thread is just incase things have gone wrong

• Help! changing admin url broke admin