Should I pray to learn my guardian angel's name?
The short answer
No. The Church discourages giving names to the holy angels, except Gabriel, Raphael and Michael, whose names are in Scripture.
The Church discourages naming guardian angels. The Directory on Popular Piety and the Liturgy (217) says devotion to the holy angels is legitimate and good but can give rise to deviations, such as assigning names to the angels, which should be discouraged except for Gabriel, Raphael and Michael, whose names appear in Holy Scripture.