"fears about getting hacked" - choose good passwords or use a password manager, keep your software and OS up-to-date, disable Java and Flash in the browser, don't visit disreputable sites.

"and having my game data stolen or deleted" - use an automated backup system like Crashplan.

"I also fear having my Steam, Kickstarter or Paypal accounts hacked" - enable Two-Factor Authentication where possible. Ensure you have recovery email addresses set up. Use the same name across the various services so that, in the event of a dispute, it's easy to prove that you are the original owner.

"What if a hacker were to show all my embarrassing past activities and postings I had on the Internet to my parents or friends? It would be very awkward for me." - What's done is done. You can't prevent that. Learn to live with it. Maybe a legal name change would reduce the chance of this happening, but it's unlikely it would ever be an issue.

"Then there’s the worry over getting doxed" - why would they want to? I'm not saying it doesn't happen to people that don't deserve it, but the quantities of people we're talking about is quite slim.

"I want to keep living my quiet, private life, but it seems like you can't if you want to hit it big. It seems like you can't make any sort of impact in the gaming industry at all, if you're not well known. What does someone do about that?" - You can develop under a pseudonym or a business name. But really, the chances of you hitting it so big that privacy becomes a problem are miniscule.

"I suffer from OCD and chronic paranoia" - this is your main problem because it's causing you to exaggerate the risks. I suggest you seek psychological or medical assistance to try and help you put things in better perspective. Most of what you're worrying about hardly ever happens, and most developers never get far enough for it to be a concern anyway.

what they do to protect themselves?

Are you asking about preventing you're online presence being hacked?

or about keeping your game from being cracked?

The first one, right?

The first is a cyber-security issue. the second is about DRM technology.

For me, the normal precautions for cyber-security have always been adequate.

I didn't have to worry about DRM until I made a game popular enough to warrant cracking. IE: it was well known enough that cracking it would bring bragging rights to the cracker, which is why crackers crack games in the first place - solely for bragging rights - they just happen to injure gamedevs in the process.

What you are trying to do is predict possible risks and asking for ways to mitigate those risks.

Here's what you need to do:

1) Write out every risk you can think of to you, your game project, your company, etc.

2) To the best of your ability, rate each risk on the likelihood of its occurrence.

3) Then, assume that each risk will happen, try to assess the impact it would have on your operations.

4) Finally, sort each risk based on the likelihood of its occurrence and the level of impact it would have on your operations.
You'll have a risk matrix which has a list of things which are high frequency, high impact, all the way down to low frequency, low impact.

You want to spend most of your efforts on the high frequency, high impact items and you want to start taking steps to mitigate those risks. You can either work to reduce the chances that the risk would happen, or work to reduce the impact it would have on your ops (or both). You won't always have a 100% fail safe solution to everything, but you can work to get something to an acceptable level.

Let's take data loss as an example of a risk you might face:
The chances of data loss are medium. A hard drive could crash. A hacker could delete files. A virus might wreck your data. Human error. etc. etc. Lots of possible sources, all somewhat low, but combined, you get a medium level threat on its likelihood. The impact would be catastrophic, so medium multiplied by catastrophic should spurn anyone into taking preventive measures / action.
So, the best you can do is reduce the impact of such an event. To mitigate this risk, you should have a backup process in place! The frequency of your backups should be based upon how much work you can afford to lose. Every minute past your last backup is data living on borrowed time, so you're only as good as your last backup. Some business systems can't tolerate more than a few seconds of lost data (think of financial systems), others can't handle more than an hour of lost data, others a day, some a week, two weeks, etc. The shorter your tolerance window, the more expensive your risk mitigation solution is going to be.

Take a good bit of time to read through this:
https://en.wikipedia.org/wiki/Risk_management

I agree that you should seek medical assistance, even if you are not mentally ill or anything. Your paranoia might be "normal" but the way you handle it (always considering the extreme bad examples; possibly having the delusion that you have serious crimes "skeletons in your closet" in your past; stating that you were a stereotypical teenager yet thinking you were special enough for anyone to care) and let it take over your life is not.

I’m also anxious about what would happen if people were to make up and spread rumours or gossip about me. Remember Phil Fish, that guy who developed Fez? When I read about how he got hacked, it scared the daylights out of me. He literally had his life destroyed in one blow. People said he had a bad reputation and was very rude towards fans. So now I’m really worried about offending consumers too.

There are thousands, if not millions of popular people (rock starts, actors, developers, company leaders, whatever) who are not being hacked and are way more interesting than a game dev. You could be more afraid if you are a politician.

And maybe you should get a communications team or at least a secretary who handles fan emails.

One common way to do this is to create a company. No, I am talking about not only coming up with a cool-sounding studio name, but a legit company that you register under you state/country. This process can take several weeks depending on how it works in your country, and may cost you some money, and be ready to pay additional taxes. Once this company of yours become a legal entity, then you operate all your game development business under this company name.

You register to your Steam account under this company name.

You open a bank account under this company.

You set your email address under this company. So, instead of draining2332@gmail.com, you put draining2332@myrealcompany.com.

You create a website under this company.

However, this does not mean that you are *fully* protected as nothing is fully protected. Anyone with crazy enough intention to dig your personal info could do so, and would eventually know that you are behind this company. But, it is enough deterrent for most people from digging through your personal info. Now, instead of plastering all your games with your real name, you put your company name. Most people don't care if they download their game from "Awesome Rock Studio".