People often have multiple social identities even in the physical realm
Authenticity and anonymity aren't mutually exclusive and that is the beauty of the internet. In the physical realm, you are (mostly) limited to a single social identity. In the digital space, there are no such restrictions. While you can't embody multiple persons in the offline world, you can have several identities online. [...]
This is, in practice, not the case. Many people have what are in effect multiple social identities in the real world, and you can even argue that the lack of support for this in common platforms on the Internet has created some real problems (especially for how people interact with them).
The way you naturally create multiple social identities in the real world is simple; you don't tell everyone you interact with about everything you do, especially in detail. You are in practice one person at work, another person at home, a third person at your bike club, a fourth person on the photowalks you do (or did) with the group of regulars, and so on and so forth. These disjoint groups of people may have some idea that you have other identities (you may mention to your co-workers that you're a keen bicyclist and are in a bike club), but they probably don't know the details (and often they don't want to). In practice these are different social identities and you're a different person to all of these groups; each one may well know some things about you that would surprise others who know you.
(My impression is that this separation is especially strong between work and everything else. People like to draw a line here and not share back and forth.)
By now, we've all heard stories of these separate social identities breaking down (or being exposed) on the Internet in social media, in the familiar story of 'I had no idea they were <X>' (or 'believed in <X>'), where <X> is often something uncomfortable to you. Before Facebook, Twitter, and the like, this sort of thing required different groups of people to talk to each other or have an unexpected connection (say, one of your co-workers takes up bicycling and joins your bicycle club). Now, social media often slams all of that together; if you see anything of someone, you may see everything. Social media generally tacitly encourages this by making it easiest to share everything with everyone, instead of providing good support for multiple social identities on a single platform (leading to the perennial 'I followed you to read about <X>, not <Y>' complaints on Twitter and elsewhere).
(You can also argue that the Internet makes it easier for people who want to cross connect your (online) identities to do so, because it made broad searches much easier. On the Internet, you have to be deliberately anonymous or simple web searches may well turn up multiple social identities.)
Relatively strong Internet anonymity is probably easier than strong physical anonymity, at least today (where you can take someone's name you learned from one connection to them and start trying to find other signs of them on the Internet). Physical social identities necessarily leak what you look like and often your name, and you can readily skip both on most of the Internet.
(Some portions of the Internet are very intent on knowing your real name, but there's still a broad norm that people can be anonymous and pseudonymous. And if you have a relatively common name, even your name is relatively pseudonymous by itself, because there will be many people on the Internet with that name.)