Should you bow your head at the name of Mary?

The Catholic Church suggests bowing the head during liturgical functions at the name of Mary as a sign of reverence and honor.

During the celebration of the liturgy, the Church suggests a variety of physical gestures that are filled with spiritual significance.

One of the more obvious gestures is the genuflection, which is only reserved to the Blessed Sacrament.

Another common gesture is the bowing of the head. The General Instruction of the Roman Missal explains the spiritual reason for this gesture:

A bow signifies reverence and honor shown to the persons themselves or to the signs that represent them. There are two kinds of bows: a bow of the head and a bow of the body [also known as a profound bow].

A simple bow of the head may be done at the name of Mary.

A bow of the head is made when the three Divine Persons are named together and at the names of Jesus, of the Blessed Virgin Mary, and of the Saint in whose honor Mass is being celebrated.
GIRM, 275

This gesture does not make the Virgin Mary equal to God, but is a small gesture of “reverence and honor.”

Dom Prosper Guéranger writes this short line to show the difference in his Liturgical Year:

At the name of Jesus every knee is bent; at the name of Mary every head is bowed.

It should be pointed out that bowing at the name of Mary is not a commandment, and is not required of Catholics.

However, for those who want to show honor to Mary in a physical way, it is appropriate to bow your head when her name is mentioned.