I don't think she is asking for people to have to use their real names to comment online, but that they should have to register for the sites under their real name, meaning action could be taken against them if they are abusive, have multiple sock accounts etc., but would still be able to use an anonymous screen name to post.
If it could be made to work, I think this would be a good compromise, as it would still protect people from being put at risk by their identity being visible (being threatened in real life/pursued at work for saying sex is binary for example!), but would allow those making threats, sending 🍆 pics etc to be identified and if necessary reported to police.
My only questions are a) how would they know whether the details given are sign-up were real/really that person, and b) people for whom anonymity is important would have to trust the social media companies both to keep their info safe from external hackers etc, and to be unbiased themselves so they don't end up pursuing people or reporting them to police for exercising reasonable free speech!
As well as the safety and privacy issues that cause so many of us to stay anonymous (and which can't be resolved just by taking away abusers' anonymity online, as the abuse can easily be taken into the real world instead if the victims' identities are known), a lot of people have jobs where they are required to watch what they say in social media if it could potentially be linked back to their employer, so I don't think forcing people to use real names to post would ever be workable!