The concept of "guardian angels" is thoroughly Jewish. Moses records human interaction with guarding angels in the Torah, and Daniel frequently mentions the powerful role of angels as guardians (see Daniel 10 for details).
Christ our Lord explicitly teaches the existence of guardian angels in Matthew 18:10: "See that you do not look down on one of these little ones. For I tell you that their angels in heaven always see the face of my Father in heaven."
The early Church Fathers also spoke of our guardian angels. St. Jerome, for example, taught that each person (both good and evil) has a guardian angel appointed to a person from the beginning of his existence.
Saint Thomas Aquinas taught that all humans have a guardian angel and that these were chosen from the lowest hierarchy of angels.
Blesse John Paul II emphasized the role of the Blessed Virgin Mary in the ministry of guardian angels:
"Let us invoke the Queen of angels and saints, that she may grant us, supported by our guardian angels, to be authentic witnesses to the Lord's paschal mystery" (Regina Caeli Audience, 1997).
Maria Agreda, the visionary, taught that the Blessed Virgin Mary had hundreds of guardian angels, including St Michael and St Gabriel. I've heard some people say that Catholic priests have "two guardian angels," but I don't know if this tradition has any magisterial support.
And to raise a very controversial topic, you're not supposed to name your Guardian Angel. Sorry, just don't do it.