The naming of a patron saint of a parish church must be chosen by the clergy and the faithful of the area in union with their local ordinary (bishop) and then approved by the Congregation for Divine Worship and the Discipline of the Sacraments.
Often the faithful of a specific region will hold a particular devotion to a particular saint, thus making the choice more easy. The bishop can not name the patron saint of a church without the aid and inspiration of local clergy and the faithful.
As an intercessor or advocate before God, the patron is a created person, such as the Blessed Virgin Mary, the Holy Angels, a Saint or Blessed. For the same reason, the Most Holy Trinity and the divine Persons are always excluded as patrons.
A patron must be chosen by the clergy and the faithful, whose choice must be approved by the competent ecclesiastical authority. In order that they may carry liturgical effect, the choice and approbation require the confirmation of the Congregation for Divine Worship and the Discipline of the Sacraments, which is granted by decree of this same Dicastery.
The patron of a place is distinguished from the title of a given church; they may be the same but are not necessarily so.
When a new parish has been erected in place of several suppressed parishes, the new parish may have its own church, which, unless it is a new building, retains its existing title. Further, churches of suppressed parishes, whenever such parishes are considered as ‘co-parishes,’ retain their own proper titles. - Patron Saints of Churches
Ultimately it is up to the local clergy and the faithful to propose the patron saint of a parish church to the bishop, who will give his approval to the motion
Nota Bene: Number 8 simply means that the title of a church may be of the Most Holy Trinity or one of the divine Persons; but since they are not Saints, Blessed or Angels they are always excluded from being the patron saint of a church.