I think anonymous social media, while still social media, occupies a very different category from non-anonymous (identified?) social media. And the default interpretation of “social media” is the latter.
That’d make Twitter not social media for people not using their actual names.
Alot of people do use their names on Twitter, and they really encourage you to follow, buy, and sell.
I don’t recall people calling forums social media, and Lemme (and Reddit) are more like forums, with you following the subject. Not each other. Very much like BBS back in the day except with links.
The tougher requirement of people using their name would leave very few social medias. Basically just LinkedIn and Facebook, with Twitter and others that have usernames but also named people being in the grey area.