How To Change A Single Page’s Header

I’m wondering how I can change a single page’s header (using Sparkling theme of course)?

More specifically, this is what I’m looking to accomplish:

==> https://screencast.com/t/rvCqTSGEMg

On this website, the header title is different to the page name… And I also want to know how to add the same search bar to the right of the title.

You help would be appreciated. Thanks!