Question: I am a masters student at one of the top two universities in the UK and will be applying for PhD positions soon. When I google my (unique) name, the first few results are what you'd expect, my LinkedIn, Twitter, Facebook, and some university web pages. 

However if you keep scrolling and go through the pages of Google's search results, you see some silly forum posts from when I was 12-14 years old, and some poorly written Yahoo Answers questions from the same time. I am now 22 so this was almost 10 years ago.

I know it's stupid but when I was that age no one really taught me how to use the internet properly and so ended up using my full name in a number of places.

I've not written anything offensive and my name isn't on anything objectively bad, but it's just childish silliness (memes, poorly written stories, Yahoo Answers nonsense, and just weird forum posts) and I'm a bit embarrassed to be honest. I feel like as I continue to progress academically, it will become more likely that people will Google me and see all this which might make it likely that I will be judged. Again, it's nothing offensive or objectionable just old young teenager stuff. Benign but embarrassing.

Should I just ignore it and hope that as my career develops these old results get pushed further back in Google's search results? Should I try to remove this stuff from the internet (very difficult as I have lost all these old accounts)?

The stuff I posted back then has little to nothing to do with who I am now professionally, and I would hate for people to think it is. Having a unique name does seem like a curse sometimes and I have made it worse by being extra foolish when I was young.

Answer: 
From what you described, I wouldn't worry too much about it. If you were *earnestly* engaging in public discussions before you had mastered articulate presentation skills, I personally would see that as a positive not a negative. But much more likely, I'm never going to search remote forum boards for a candidate I'm interviewing. 

With that said, I think a very proactive measure one could take is to simply build a professional website. If I'm interested in judging the professional contributions of an individual, this is the very first and most likely the last place I will look for them; it gets straight to the point and typically communicates exactly what technical skills they do (or do not) have. If I'm interviewing you, I don't care if you're into sky-diving in your free time, I want to know what your research interests are and how well you communicate technical information. A website is a great place to demonstrate this. 

As an anecdote, I also have a unique name (only one in the world) and for a long time if you Googled me, my website was the first result to pop up and some combat sporting events I participated in would pop up on the first page of the search results (it's now moved down much further). At the time, I similarly was slightly embarrassed, as I felt it was a bit unprofessional. Many of the people who have interviewed me were familiar with what was on my webpage. Not a single one was familiar with the sporting events.
Relax.

What you did in your 12 is half your time here back. It will become a third soon, quarter slightly later, etc.

During this time you will feed the Internet with new and more relevant content and low-quality posts will become very obsolete and cannot backfire to you. If anyone tries to play that card in an argument, you can belittle it by "And you were a genius in your 12? You made a very poor improvement since then."

The only case your 12-year-old self can backfire at you is a very serious misbehaviour and it still can be dismissed as "I've learnt my lesson from that".

This is the part of growing up and learning. If you don't learn you don't improve. What actually happens to you is judging your old posts written with 12 year old knowledge and 12-year-old skills by criteria adjusted to recent knowledge and 24-year-old skills. Be sure that after 10 years you will see your today's work, you are proud of, with the same emotions as you are seeing the ancient posts Google has found.

If you are about to be assessed by a sane person they will know that and ignore that. If they will assess you because of your 20 years old posts, it is a strong argument for you to never meet them again.