Copy customer.xml
to your theme (if it's not there already). Then remove OR comment below line:
<action method="addLink" translate="label title" module="customer"><label>My Account</label><url helper="customer/getAccountUrl"/><title>My Account</title><prepare/><urlParams/><position>10</position></action>
For changing Name/Title
, you can update the values of above xml's
<label>
and <title>
tags, like:
<action method="addLink" translate="label title" module="customer"><label>CUSTOM NAME</label><url helper="customer/getAccountUrl"/><title>CUSTOM NAME</title><prepare/><urlParams/><position>10</position></action>