According to the other sources Pilate was markedly anti-Jewish, cruel and incompetent. In the year 36 CE, he was removed from his function by the emperor, a very unusual measure.
This exile of Pilate could have originated the legend of a conversion of Pilate, his own realization of his errors as governor.
Hence, this legend was annexed by 'Mark' (author) to explain the independent legend of a Jesus crucified by Romans.
And the name of Pilate entered in his story.