Samuel Beckett's Dante and the Lobster is a story about a young poet with much heart, but little confidence, who has to learn how to emerge from his own inconsistent world to find his voice. It alludes in a good part, and it is inspired by, Dante Alighieri's The Divine Comedy not only in the naming of characters, but in adding parts of the Divine Comedy to the original plot.
The specific part of the story to which you refer can be found in the beginning where it reads,
It was morning and Belacqua was stuck in the first of the canti in the moon. He was so bogged that he could move neither backward nor forward. Blissful Beatrice was there, Dante also, and she explained the spots on the moon to him. She shewed him in the first place where he was at fault, then she put up her own explanation. She had it from God, therefore he could rely on its being accurate in every particular.
It is understandable for this fragment of the story to be confusing, as it is taken directly from the storyline in Dante's Divine Comedy. It refers to the part of the story where the poet, Belacqua, is enthralled reading the Divine Comedy. What Beckett is stating in that part of the story is that both Dante AND the very blissful and beautiful Beatrice from the story were in his thoughts, specifically during the part of the Divine Comedy where Beatrice shows Dante the Kingdom of Heaven.
Historically and literary speaking, the "Blissful" Beatrice refers to Dante's love interest in the Divine Comedy, who is, in turn, inspired by Dante Alighieri's one and only true love, Beatrice Portinari (1265-1290). Dante's personal love story basically states that this lady, Beatrice, was someone whom Dante loved so much (they never got married) that he opted to name his Divine Comedy heroine after her. In the Divine Comedy, the character of Beatrice is who points to Dante to heaven, and who explains the bliss of Paradise and eternity. Her character represents, love, purity, grace, and beauty. This is why Beckett refers to her as "blissful".
Therefore, in summary. Beatrice is a character in the Divine Comedy, inspired by a real woman named Beatrice whom Dante loved. There is no character in Dante and the Lobster named "Blissful Beatrice". The word"blissful" is merely used as an added adjective by Beckett to refer to the original Beatrice's lovely life as an angel in heaven.