For changing the url of admin from our existing magento store there are two methods we have:

Method 1- First Go to app/etc/local.xml file , open this file with an editor .Now find for the admin node where you have to change the frontName to our chosen url there.

Example : - Here we have changed admin url to new name that is adminpanel .see the below code.

<admin>
    <routers>
        <adminhtml>
            <args>
                <frontName><![CDATA[adminpanel]]></frontName>
            </args>
        </adminhtml>
    </routers>
</admin>

Method 2- Second way way for changing the admin URL is by using admin panel of Magento

Please go to the defined path i.e. System -> Configuration->Advanced ->AdminAdmin Base URLUse Custom Admin URL

Now set it to 'yes' and after then please enter the new admin path in the text field named as Custom admin path and finally step is save this change.