Facebook and Google+ tried to do this with their realname policies. It doesn't work as well as one would expect:
• Toxic assholes are not deterred by their name being attached to what they're saying, because they think they're saying righteous things and/or fighting bad people who don't deserve any respect.
• People self-censor, because they don't want to risk upsetting some random violent stranger on the internet who can track them down.
• People who don't use their legal name publicly have trouble participating. This impacts transgender people, but also people using stage names/pen names, and stalking victims.
I think OP's point isn't to prevent toxic assholes from saying whatever righteous things and fighting whatever bad fight, but to limit bot/inorganic/foreign contributions from made up people - basically to make it "one person one voice".
I kind of like the idea of "one person one voice", but I have two problems with it, which I think will block me from accepting it.
One is that the cost of it seems much too high, even if you can change it to allow the use of chosen aliases (I don't think it matters what a "one person one voice" system calls an authenticated member). I don't really trust everyone who I have to give my ID details too, and this is just one more bit of stress for so little gain.
The second is that the benefits will never be realised. In an election, one person one vote doesn't work when half the population doesn't vote; you need almost everyone to come, otherwise it's the strongest opinions not the mainstream opinions that dominate. And I'm quite sure we'll see the exact same thing here, but in spades, and faster. If you don't like the opinion, you just don't show up. Once the centre of the social media is sufficiently different from the centre of the community, there will be the sort of bullying and self censorship you foresee and it will spiral out of control.
There's no need for real names, what is needed is that you can't create multiple accounts. This can be done without linking identities by using two unrelated parties. Party A is the platform and B is the authenticator, when creating an account on A you are sent to B to authenticate your identity and get a token to finish your account creation on A. As long as A and B are separate, A never knows the identity of the user and B doesn't know what the user represents himself on A.