Does each person have a guardian angel, and if so, should the person assign him a name?
11 For he will command his angels concerning you
to guard you in all your ways;
12 they will lift you up in their hands,
so that you will not strike your foot against a stone.
10 ‘See that you do not despise one of these little ones. For I tell you that their angels in heaven always see the face of my Father in heaven.
Catechism of the Catholic Church
336 – From its beginning until death, human life is surrounded by their [angels] watchful care and intercession.202 “Beside each believer stands an angel as protector and shepherd leading him to life.”203 Already here on earth the Christian life shares by faith in the blessed company of angels and men united in God.
203 St. Basil, Adv. Eunomium III, I: PG 29,656B.
204 Gen 1:l-2:4.
Should we assign names to our guardian angels?
The Congregation for Divine Worship stated in its document Directory on Popular Piety and the Liturgy:
Chapter 6, Paragraph 217
The practice of assigning names to the Holy Angels should be discouraged, except in the cases of Gabriel, Raphael and Michael whose names are contained in Holy Scripture.
Guardian Angel Prayer
Angel of God, my guardian dear,
To whom God’s love, commits me here,
Ever this day be at my side,
To light and guard, rule and guide.