Googling my name reveals silly things from when I was younger. I am embarassed. How will this affect me in my future academic career?
I'm deeply involved in web technologies, including search results. The simplest and fastest way to solve this problem is to add other search results. The more "legitimate" and positive results found, the less likely the others will be seen. There are numerous factors in raising search results, but still:


Create another Stack Exchange account with your name and use it. 
Create social media accounts with your name. 
Join groups and use your real names (in addition to pseudonyms). 
Create a Disqus account with your name.


You don't need to make many posts on each site, but place professionally enhancing content there.

If you really want to spend time with this - open other accounts with simple variations of your name thus creating even more false results. 

A little work every day and soon you'll have 100s if not 1000s of positive results that will appear above the other silliness.