You have to insert anotger function fot the second post rename like
function rename_post_formats_2( $safe_text ) {
if ( $safe_text == 'Link' )
return 'NewTip';
return $safe_text;
}
add_filter( 'esc_html', 'rename_post_formats_2' );
before
//rename Aside in posts list table
function live_rename_formats() {
global $current_screen;
if ( $current_screen->id == 'edit-post' ) { ?>
<script type="text/javascript">
jQuery('document').ready(function() {
jQuery("span.post-state-format").each(function() {
if ( jQuery(this).text() == "Aside" )
jQuery(this).text("Tip");
});
});
</script>
<?php }
}
add_action('admin_head', 'live_rename_formats');