He was Beatle George, he was solo George.
But he was always George Harrison, musician.
He may not have known all the chords . . . but he knew "a lot more than we knew," as John Lennon said, remembering the day in 1957 when Paul McCartney introduced him to George Harrison. And that was enough for John to agree with Paul that George should join them in the band that would eventually become, with Ringo Starr, the Beatles.