Digital Spy is reporting that "Peter Capaldi" is the 11th most searched term. They further detailed that one in every 340 searches involved the word "Capaldi", one in every 300 involved "Doctor" and 1% of all searches were linked to Capaldi or his casting. Given that the show was viewed by over 6 million people (most of whom run to Google to find out W.H.O. he is), this is not surprising, but good news none-the-less.
They also provided some comparison figures, with the immense international Royal Baby news accounting for 3% of searches and Jessica Ennis-Hill managed 1% when she won gold at the London 2012 Olympics.
While the validity of a third-party tool cannot be confirmed, Google's own Google Trends service states "Peter Capaldi" at the #1 trend with over 2,000,000+ searches.