Star Wars: The Last Jedi resolved a lot of key mysteries - what happened to Luke, who Rey's parents were, whether there were other colors of milk in the galaxy - but one of its key backstory reveals was a little more subtle: how Kylo Ren created his lightsaber.
Kylo Ren's lightsaber choice has been debated since before we even knew the character's name; the crossguard saber's reveal in The Force Awakens teaser all the way back in November 2014 courted backlash thanks to its cracking blade and questionable practicality. Of course, in the years since it's become very much accepted, a striking summation of the character's fractured psyche that stands as iconic as Darth Maul's double-bladed lightsaber from The Phantom Menace. The crossguards have even been put to good use, with Kylo using them to injure Finn during their mismatched duel on Starkiller Base.
In The Last Jedi, we got to see Ben Solo wield a different looking saber: his blue blade from his training at Luke's Jedi Academy, used to defend himself from his uncle's supposed attack. Just as the question of what happened to the elder Skywalker's green saber from Return of the Jedi (the novelization suggests it was on Ahch-To all along), there's been much discussion of what happened to the apprentice's blue saber. Now, thanks to the home release, we have a good idea: he turned it into the crossguard saber.
How Kylo Ren Turned His Jedi Lightsaber Into The Crossguard Weapon
Putting them side-by-side, Ben Solo's training lightsaber definitely looks to be the same hilt as Kylo Ren's crossguard weapon with several modifications - it's got the vents, of course, but is a charred black and has exposed technical elements. That they are identical isn't stated explicitly anywhere in the canon, although beyond aesthetics, The Force Awakens Visual Dictionary does provide some light on Kylo's saber creation, saying "Though Kylo's weapon evokes an ancient feel, its components are modern." The implication is that Kylo evoked classic Jedi/Sith designs (a more elegant crossguard saber was seen in Star Wars Rebels) by bastardizing his weapon.
Although the change may also be in response to the kyber crystal within. We know from the Darth Vader comic that Sith turn their crystals - and thus saber blades - red by a process known as "bleeding"; a dark side Force user tarnishes the crystal with their hate. This is how the synthetic blades are created and must be what Kylo attempted. However, something went wrong: his crystal cracked, leading to the crackling blade and need for vents. It's possible the modifications are all an attempt to keep the weapon stable.
One of the best meta-elements of the sequel trilogy has been how Kylo Ren operates a Star Wars fanboy parallel - he cosplays in his helmet, collects Darth Vader memorabilia, and even has his own fan club (the Knights of Ren) - and this homemade adaptation of his lightsaber serves as a more visual example of that. He tried to mirror his grandfather only to fail, yet in doing so created something more unhinged and dangerous; just like his actions in The Last Jedi.