I can't begin to piece together exactly what's happening in the finale, despite watching episode 18 twice last night and having my subconscious mull it over for eight dream-state hours. I don't, however, agree with the cut-and-dry notion that this is simply another story or an alternate timeline. Here are some random thoughts that I hope will coalesce as the days go by and we all delve into discussion:

(1) Phillip Jeffries' dialogue with coop and the 8/infinity loop are important keys to understanding what's going on. There are some cryptic hints here ("It's slippery... He'll [Gordon] remember the unofficial version... did you ask me this" etc.)

(2) Time. Cooper requests 1989 from Jeffries, but when He and Diane hit 430 and crossover, the date is clearly earlier. The car they drive, the motel, and the decor, including the rotary phone, all hint to something well before 1989, likely the 1960s. 

(3) Richard and Linda. Everyone is assuming that Cooper and Diane are now other people, or somehow subsumed by this new "story," but I don't necessarily think so. When Coop wakes up, everything is entirely different, but he remembers who he is. He finds the letter and seems surprised, and everything has changed: the motel, his car, the timeline. 

(4) Coop is still himself, but as an amalgam of his different versions (Mr. C, Dale, Dougie). He has purpose. He remembers Laura, Twin Peaks, etc. He is calculated, intuitive, and effective. 

(5) There are signs that Laura is still there, somewhere inside of Carrie Page. We see the white horse on the mantle in her home. She has a very odd reaction to hearing that her mother's name is Sarah, as if she remembers, but doesn't understand. Then she hears the FWWM "Laauuuurraa" and screams at the end. 

(6) The telephone pole with the number 6 is there again. Outside Carrie's home in Odessa. We've seen this before, always when trouble is afoot. We see it in the Fat Trout trailer park in FWWM, in conjunction with the Arm's sound, in Deer Meadow, Oregon. We see it again in TPTR at the new Fat Trout trailer park in Twin Peaks. 324810, #6. 

(7) The finale is titled "What's Your Name?" and we now know that the answer is "Alice Tremond." In my opinion, the Tremonds/Chalfonts are the key to this entire mystery. They owned the trailer where Desmond finds the green ring. They give Laura the magic painting which allows her to enter the convenience store/lodge. They are present at the Convenience Store meeting which Jeffries observed. They are there when Leland sees Laura with Theresa Banks in FWWM (the grandson comes jumping out of the bushes). Mrs. Chalfont tells Donna that her grandson is learning magic. He manipulates reality, by snapping his fingers, teleporting the creamed corn into his hands from across the room. He seems to know the future when he says, "J'ai une âme solitaire," which would later be found in Harold Smith's suicide note. He wears the jumping man's pointy mask. Is it a coincidence that the jumping man character returns several times in TPTR, preceding time/dimensional shifts? In the original Twin Peaks, when Donna brings Coop back to the Tremonds, they are mysteriously gone and an entirely different Mrs. Tremond exists in their place, much like the ending scene in the finale. 

There is a LOT to unpack here, but I've been thinking about what Laura says to James in FWWM and reprised in the S3 finale (ep17): "Your Laura disappeared." What if the real Laura followed Mrs. Tremond into the painting in FWWM, and a tulpa version of Laura came back? In that scene, the arm tells Cooper what sound he makes (again reprised in the finale), and Annie says, "I've been with Dale and Laura. The good Dale is in the lodge..." Why would she say "I've been with Laura" to Laura? 

Also of note, later in FWWM, just after the scene where MIKE confronts Leland in the intersection, Laura thinks back to it and the green ring, realizing that it's the same one Theresa Banks wore. There is a slow shot of the clock changing to 8. 

Your thoughts, on any of this?