Google.com is not providing any direct way to change the google logo or change google logo name. Google Logo Maker is site where you can make google logo. This site is not a part of google.com, but its search results provided by this site are same search results as provided by google itself because it use Google custom search.
Google logo maker is as simple as 1,2,3…. Just open Google Logo Maker, enter the name, select the style(option button) you like and here is your own search engine with your name or your lucky name as google logo. So, why you are waiting just start making google logo now.