WRT to search results, let Google update its search results, once done, you should be able to get the new name appearing in search results. Indexing and updating results takes a bit of a time.
I was reading https://support.google.com/youtube/answer/2657964 and in the end it says:
Note that it may take some time for the changes to update throughout the site.
I guess all you need to do is wait for sometime.