try switch to the main blog where buddypress is installed, echo the profile fields then switch back to the current blog.
$bp_blog = 1; // the blog id of your buddypress install, often 1
switch_to_blog($bp_blog);
echo bp_get_profile_field_data( 'field=Name');
restore_current_blog();
if that doesn’t work, maybe the user in question is not a member of your main blog. You might need to add all users in the network to the buddypress blog if they are not already.