However, where things get blurry is the very early history of this forum. We can see Satoshi's posts, but were they actually made here? Or were those posts imported from elsewhere like SourceForge? The piece in question has to do with this forum's domain name only being registered in 2011. But again I might be lacking historical context.
Originally this forum was part of bitcoin.org; you can see it on the Wayback Machine existing as such:
https://web.archive.org/web/20110519220748/http://forum.bitcoin.org/It moved from forum.bitcoin.org to bitcointalk.org in 2011.
When satoshi says "Welcome to the new Bitcoin Forum!" in his first post (or 1st non-deleted post) he was referencing SourceForge as where a different forum initially existed for a short time beforehand.
Technically, this forum, whether on this domain or bitcoin.org, has always been called the Bitcoin Forum, as you can see in the top left of every page.