When Giovanni first comes across Rappaccini's garden, the story calls attention to a statue of "Vertumnus," which is an allusion to the god of change and the seasons in Roman mythology:
One plant had wreathed itself round a statue of Vertumnus, which was thus quite veiled and shrouded in a drapery of hanging foliage, so happily arranged that it might have served a sculptor for a study.
In Ovid's Metamorphoses, Vertumnus seduces a wood nymph, Pomona, by disguising himself as an old woman in order to gain her trust, enter her orchard, and convince her to marry him. Like Pomona, Beatrice is a young woman who is very much in touch with nature, as she's devoted to caring for the plants in her garden. Both women are enclosed in a natural haven that excludes men. Like Vertumnus, meanwhile, Giovanni inveigles his way into this haven and seduces the woman he desires.
By drawing these parallels between Beatrice and Pomona (and between Giovanni and Vertumnus), this allusion foreshadows Giovanni's seduction of Beatrice. Of course, unlike the story of Vertumnus and Pomona, in which the former's deceit culminates in a happy marriage, the story of Giovanni and Beatrice ends in misfortune and tragedy.
In "Rappaccini's Daughter," the character Beatrice’s name is an allusion to the Divine Comedy, a long narrative poem by the Italian poet Dante Alighieri that follows the poet himself as he journeys through hell, purgatory, and paradise. This allusion in "Rappaccini's Daughter" adds some insight into both Giovanni's and the reader's initial uncertainty about whether Beatrice is good or evil. In the Divine Comedy, Beatrice serves as Dante's deceased love interest and guide in the final part of the Purgatorio as well as the Paradiso. In Inferno, she's the one who sends the famous ancient poet Virgil to guide Dante through hell, wanting to make sure he's protected on this leg of the journey so that he can eventually join her in heaven. She is, then, presented as the pinnacle of moral purity, grace, and femininity.
Beatrice's name initially seems ironic, given our suspicions that she is complicit in the unknown evils of Rappaccini's garden. And yet, the more we see of Beatrice, the more fitting her virtuous namesake comes to seem: she even crosses herself over the death of an insect. In this way, Beatrice's name suggests her moral purity even before the story confirms that she is not intentionally poisoning Giovanni. Ultimately, Beatrice's name, with its allusion to Dante's heavenly guide, emphasizes the irony that Giovanni could deceive himself about someone who is so obviously good rather than evil.