Commentary Purg XIX 28-30

If this is Beatrice, then it is hardly surprising that she would recognize Virgil, in the dreamer's estimation, since he knows from what he was told in [Inf II 53] that Beatrice came to Virgil in Limbo.  And as for the identity of the lady here, characterized as being 'onesta' (virtuous), it is probably worth remembering that Beatrice is later compared to a 'donna onesta' (chaste lady) in [Par XXVII 31].