Ever since the title announcement was a pleasant surprise for the millions of viewers desperate for any and all information they can get about the hotly anticipated sequel. This is obviously just the tip of the iceberg, but it's more than enough to kickstart the next wave of Star Wars theories and speculation.
Looking back at the history of the franchise, the names of the films often hold a great many clues about its main story and/or themes. For example, The Force Awakens referred to Rey realizing her powers and abilities, while Rogue One is the call sign used by Jyn Erso's team as they go off to steal the Death Star plans. So, while The Last Jedi is far from an official synopsis about the movie's specifics, it at the very least serves as an indicator of what Johnson and the Lucasfilm story group have in mind for December. Often times, the movie titles are quite obvious in their meaning (The Empire Strikes Back), so we're analyzing the title and the possible directions the story can go.
At first glance, it's very apparent Luke Skywalker is the main subject of the title. After all, the Episode VII opening crawl mentioned Luke was "the last Jedi," and the First Order would not rest until he was killed. It's true Rey is starting to tap into her potential (and will likely follow the Light Side of the Force), but for the time being Luke is the only Jedi Knight in the galaxy. Based on information relayed by Han Solo in The Force Awakens, Skywalker was attempting to rebuild the Jedi Order before Ben Solo became Kylo Ren and ruined it all. Johnson has gone on record stating the relationship between Luke and Rey will be "a large part" of the film, so it isn't surprising that Star Wars 8 has a title heavily based on Luke and his standing in the universe. He is going to be a primary focus of the movie, and The Last Jedi certainly reflects that.
Of course, Star Wars fans are well aware that the word "Jedi" can also be plural and has been used in the films that way several times. This means that there could be more beneath the surface; occasionally, Star Wars titles can have dual meanings. An argument can be made that The Force Awakens also covers the darkness brewing inside Kylo Ren (who was feeling the pull of the light early in the film). With this in mind, it is possible that The Last Jedi references Rey as well. It's important to keep in mind that the sequel trilogy is telling her story, so it ittedly would be strange if the middle chapter's title did not pertain to her at all. Rey is (presumably) starting her Jedi training in Episode VIII, which means she'd be following Luke's teachings as his Jedi apprentice. In that case, the title would mean Luke and Rey are collectively the last Jedi with no one else to follow their lead (depending on how the tutelage goes, of course).
Building off of this, there might be something else at play here. Luke's post-Return of the Jedi activities are deeply shrouded in mystery, but there are some small hints scattered throughout the new canon. In the novel Bloodline, it's written that Luke is journeying across the galaxy (with a pre-Dark Side Ben at his side), not the clear-cut good guys the movies make them out to be. If Luke discovers any proof of that in his adventures, what impact would that have on him and his personal beliefs?
Just looking at the previous saga installments, the Jedi have a history of failing. Their blindness (and arguable arrogance) is what led to the rise of the Galactic Empire and fueled Anakin Skywalker's turn to the Dark Side. The main reason Luke survived the Galactic Civil War is because Darth Vader had a last minute change-of-heart and killed the Emperor, not because of Obi-Wan's wisdom. And, it goes without saying, Luke was utterly unsuccessful as a teacher, a fact that led to the fracturing of the Skywalker family and the death of his best friend. This all raises interesting questions about whether the Jedi way is really the right path to follow. Luke could be the last Jedi by choice, fearful of what might happen if their traditions continue. It's largely unknown what he's been up to in the 30 years since the Battle of Endor, but he's probably concerned he does more harm than good if he flew away to a remote world. Even if he reluctantly agrees to train Rey and/or re the fight against the First Order, he may not want the Jedi to continue en masse.
Of course, fans will learn more about The Last Jedi as the marketing heats up over the coming months, complete with trailers and TV spots that hint at the storyline and plot points. For the time being, there is no shortage of possibilities, and it will be interesting to see what exactly Johnson has in store. Star Wars titles are basically simple, but there's always a definitive reason for why they're selected and typically have strong implications for the franchise moving forward. Luke Skywalker is the last Jedi, but there's a thematic purpose behind the title as well. Until the first teaser premieres, fans have no choice but to hypothesize what that is.