If you've logged onto a system and accessed the internet with a web browser, and if you've done anything on the host system where you have associated your real name or other personally identifiable data, even if you log onto other sites using a pseudonym, you have no expectation of anonymity - aka: being left alone.
If you shop online with your real name, and then proceed to make racist rants on a subreddit with a separate web login- then you have no claim to privacy or anonymity.
If you have multiple email accounts on your system and one of those accounts is your 'real' account, the rest are for 'anonymity' while you make crazy posts.... then no, if someone wants to trace you back, they probably can.
Say that you have an extra computer, and you do your anon trolling stuff only on that system, but you have other computers behind your firewall that are used for normal business stuff, w/o special lockdowns on the router, you still don't have privacy. If you connect your personal smartphone to your wifi... same thing, someone would eventually be able, with some tracking and minor hacking, to correlate your fake accounts to your real identity.
All of the stuff above gets much, much easier if you have ever had an account on any social media platform... And the more you use that platform, the easier still that it becomes.
This notion that you can have an expectation of being anonymous on the internet is nearly impossible given the way that most of us usually use the internet.
The people who are truly anonymous online are doing their work in office environments where they are using systems that highly segregated and protected from each other... lots of locked down and one-way ports on the router, as well as isolated subnets. I say "work", because those people who have access to these systems are very intentional in how they use their anonymous access. In other words, they are spies or work with spies.
If you use a computer online, like 99.999% of people use their computers, you and all your alternate ID's can be tracked and correlated by someone with some pretty basic doxxing tools. And CNN no doubt consults with a well paid 'web security' company that perform these services for them. They knew "HansSolo's" identity pretty quickly, and then spent a few hours making the confirmation. Very early on, this guy knew his cover was blown which was why he also realized he was so screwed so fast.
Even here on politiforum... no privacy or anonymity to someone really wants to find us. We throw off trackable data just by being on online. Collect enough of it over time and your privacy is gone if someone really wants to track you.
Want to be anonymous... stay off of a computer or smart phone - don't even let it into your house.