* Possible Candidates:
* Minerva McGonagall: While she is the headmistress in the epilogue, it's highly unlikely she'd continue to hold both roles. She likely would have appointed a deputy to handle the daily administrative tasks.
* Pomona Sprout: She is a senior professor and the head of Hufflepuff, making her a logical choice.
* Filius Flitwick: As the head of Ravenclaw and also a senior professor, he could have been considered.
* Severus Snape: While he died during the Battle of Hogwarts, it's possible he had a successor in place before his death.
* The Likely Answer: It's most likely that Minerva McGonagall appointed a deputy headmaster to help her manage Hogwarts. However, the books don't provide us with a specific name.
Note: There's a strong possibility that Rowling might have mentioned this in interviews or other supplementary materials, but the books themselves don't explicitly answer this question.