Just like other Jewish boys, Mary's child underwent circumcision eight days after his birth. At the same time, he was given his name: Jesus.
The gospel of Luke mentions neither the location nor the person that performed the act. In art, the episode is usually set in a temple, with a priest holding the knife.
Related works of art:
Dürer, Albrecht: Seven Sorrows: The Circumcision (1495-1496)
Mantegna, Andrea: The Circumcision (1462)
Rembrandt: The Circumcision (1661)