BuddyPress.org

Yeah, I was in midst of correcting that hopefully before you saw it. Haste made waste.

function my_adminbar_name () {
global $bp;
echo '<a>root_domain . '" id="admin-bar-logo">Welcome Connect</a>';
}
remove_action('bp_adminbar_logo','bp_adminbar_logo');
add_action('bp_adminbar_logo','my_adminbar_name');

EDIT – Works when you put this in your active theme’s functions.php file (instead of the bp-custom.php file in plugins directory as mentioned above. Thanks to @DJPaul in this post).