Abbi, most likely short for Abbigale, was a girl Greg knew from his past.
Greg released his book Stones To Abbigale in 2015. The book revolved around Greg's self-insert character, James and his high school girlfriend Abbigale. He revealed he based the character of Abbigale off of a girl named Abbi he knew.
Greg says he wrote the real Abbi the same confession/love letter his character James wrote to the Abbigale character in his book. Greg says Abbi was a cutter and had a verbally abusive boyfriend, similar to his character. (Source)
Unlike all of his other past crushes and exes, Greg never wrote about his crush Abbi on any of his old websites. Suspiciously, this includes his 2005 "Digging Deeper" Onision.com page, where he listed important people he had known, or his 2005 "A Life's Story" page, where he listed important relationships he had. (Source) Greg also had never spoken about Abbi in videos prior to writing Stones To Abbigale.
In 2019, it was revealed Greg and his spouse Kai had legally changed their names. Due to the name change records being public, it was revealed one of their children's middle names was Abbigale before the name change. This was considered odd by some since Abbigale was the name of Greg's past crush and because Greg had stated Kai hated the character Abbigale from his book. (Source)