As for the books, I'd have to check. However, just look at Bakker's personal websites (not the fan made ones):
His "newly" built author website:
https://secondapocalypse.ca/ (built by Scott and his brother Brian)
Not only is the website's url secondapocalyse, The Second Apocalypse is used all over the website when refering to all the books - Its even the website title ("The Second Apocalypse by R Scott Bakker") on the loaded page and the descriptive text on the browser tab. Even the first sentence on the home page: "This trailer showcases many of the aspects of
the Second Apocalypse that make the
series unique." It is describing the Second Apocalypse trailer which is a trailer of the entire series, from TDTCB.
Farther down on the page:
" Though you'll be missing out on an amazing back story it is possible to join the
Second Apocalypse saga at book four.
The picture to left features
Second Apocalypse Author Scott Bakker co-hosting... "
Or his blog
https://rsbakker.wordpress.com/There is a link up top that say "
The Second Apocalypse Trailer"
Up in Stories there's two headers:
(1) Atrocity Tales (short fiction set in the world of
The Second Apocalypse)
(2) Short fiction unrelated to the world of
The Second ApocalypseAlso on TPB, check out his about page, its all over that as well
https://rsbakker.wordpress.com/about/ :
"...the centerpiece of my project is
The Second Apocalypse, the tale of a monastic outcast who rises from obscurity to ..."
Edit:
Checking out some of his oldest interviews. Back in
2004 Bakker said:
How many books are you planning on writing in the PoN Universe? Also, are there any other writing projects you're considering in the near future?
I'm presently working on The Thousandfold Thought, which concludes The Prince of Nothing. Following this, I have a draft of a near future thriller entitled Neuropath, which I hope to gussy up and shop around before returning to fantasy, which is my first love.
When I originally conceived the whole story (The Second Apocalypse) way back when, it was a trilogy with The Prince of Nothing as the first book, The Aspect-Emperor as the second, and The-Book-that-Shall-Not-Be-Named as the third. But of course The Prince of Nothing has since become a trilogy in its own right, which would seem to suggest that The Second Apocalypse will be nine books long! I honestly have no idea how long it will ultimately be. My best guess is that The Aspect-Emperor and The-Book-that-Shall-Not-Be-Named will both be dualogies - if that's really a word...
my bold.
I'm sure there's more.
Its really all over everything Bakker has done or put together in at least the last 15 years . I'm not going to go all the way back to the derelict Three Seas forums to check references there. I'm also pretty sure he's used the name himself in the various Q/As he did here/reddit/other-forum but I'm less sure about that.
Regardless, "just a fan name" is definitely a gross misinterpretation. If its not clear from the books, that's definitely Bakker's fault though, not yours.