Last Updated September 5, 2023.
Explicitly in Pope's verse "Eloisa to Abelard," Eloisa and Abelard are the only characters (though one could argue God is invoked in such a way as to become a character, as well). However, this verse was inspired by actual historical figures Héloïse and Peter Abelard.
Héloïse was a renowned scholar in France, held in high regard for her intelligence. There are some conflicting details about Peter Abelard's timeline and career moves, but we know he was a philosopher and a canon (a priest with cathedral affiliation, a higher and more well-regarded position in church hierarchy). Héloïse was in the custody of her uncle Fulbert, and she met Abelard due to Fulbert and Abelard becoming canons at the same time in Paris. Abelard needed board and offered to tutor Héloïse in exchange for payment in order to stay with them.
It was during this arrangement that the affair between Héloïse and Abelard began. Héloïse eventually became pregnant (they had a boy named Astrolabe, but remarkably little is known about him, considering the amount of historical documentation that exists between his parents), and Abelard sent her to live with his sister. They wed in secret, and he wanted the marriage to remain a secret. The details of this are not certain, but there is speculation that it was due to the church's increasing rules regarding marriage and the priesthood, and Abelard did not want his relationship to interfere with his career advancement. He even convinced Héloïse to enter a convent, and they lived separate lives.
Fulbert did not approve of this arrangement, thinking that it was merely a way to be rid of Héloïse, and began to gossip, eventually leading to some tarnishing of Abelard's reputation. Family of Héloïse then assaulted Abelard and castrated him. Abelard and Héloïse continued out their lives in vocations within the church, working quite closely together, as Abelard's monastery eventually absorbed Héloïse's order. Their surviving letters detail not only their differing views of their relationship, but also the nature of love, as well as grappling over theological perspectives.
Pope's poem does not take into account much of the details of the historical figures' lives, but uses the story as a framework from which to write his verse. The poem is not only an imitation of Héloïse's letters, but is actually based closely on another poet's (John Hughes) work and is an imitation of an old Latin poetic genre. His version of this famous tale is considered to be a seminal work in bringing about the Romantic movement.
In the reference link below, I've pointed toward the eNotes study guide for the Historia Calamitatum, which is the first in the series of primary documents (written by Peter Abelard) that establishes the history of this relationship.