BuddyPress.org

Simply, create a child theme, copy the members/single/profile/ edit.php to

yourchild-theme/members/single/profile/edit.php

Now modify it slightly,

Like put his before the first line of edit.php

<?php if(bp_get_current_profile_group_id()==1)>

<ul class="button-nav">

<?php bp_profile_group_tabs(); ?>

</ul>

<div class="clear"></div>

<?php

locate_template(array("members/single/profile/profile-loop.php"),true);?>

<p><b>Your Username is your identity and We hate to see you changing your identity, so our computer has decided to disable editing it for you.Please Edit all other data in your profile as you wish 

</b>

</p>

<?php

else:?>

and at the end of Edit.php put this line

<?php endif;?>

Now go and check your profile page.

please let me know if it works or not