Anna was his ex wife. His former hit You Better Move On (see there) was another comment on their broken relationship.
Anna (Go To Him) is one of the covers on Please, Please Me, the Beatles' debut album. Their singles were always originals, but fifty percent of their earliest lp's consisted of covers. In their Stu Sutcliffe years The Beatles had more A. Alexander songs on their repertoire: Where Have You Been and Soldiers Of Love. This black Alabama soul singer was also the man behind You Better Move On, known from Rolling Stones- and Mink DeVille versions. Ry Cooder covered his Go Home Girl and then there were The Drifters, The Bee Gees, Dusty Springfield and Tina Turner to cut one or more of his tunes. According to rock critic Michael Gray, Arthur Alexander can even be regarded as the one who introduced the word 'girl' in song lyrics: Dream Girl, Go Home Girl, The Girl That Radiates That Charm, Pretty Girls Everywhere. Strange coincidence to find a similar list among Beatles-compositions: Thank You Girl, Another Girl and Girl tout court.