On the issue of anonymity, I think you are entirely correct in how you've kind of diagnosed it. Our public square is more socially located and more democratic, in a sense. If you go spout off in your local Starbucks or Tim Hortons or whatever, you might be held socially responsible for it, whereas you are not online. Of course, now we have the social media companies that are very much not a democratic space. They can make unilateral decisions over who gets to speak, and how and when.
On the issue of anonymity, I do very much take your point that people are more likely to troll and be abusive anonymously. However, we have to look at the case of perhaps a trans teenager whose parents are not supportive and they're looking to connect with a community online. Anonymity for them is safety, as it is for a woman who is perhaps fleeing a domestic violence situation who wants to engage with a social network online. In some cases, anonymity is absolutely the most valuable thing to people who are vulnerable. In the case of individuals overseas as well, where they face very real and very direct persecution by the government, anonymity is the only thing that keeps them safe.
So I don't think making the Internet not anonymous is necessarily the way to go, because there are all these cases where it has unintentional consequences on people who do need safety.