Yes. This name "Father," whereby paternity is signified, is the proper name of the person of the Father because it is paternity which distinguishes the person of the Father from all other persons.
Among us, relation is not a subsisting person. So this name "father" among us does not signify a person, but the relation of a person.
In God, however, it is not so; for in God the relation signified by the name "Father" is a subsisting person.
Hence, as above explained (Q29, A4), this name "person" in God signifies a relation subsisting in the divine nature.
In human nature, a word is not a subsistence, and hence is not properly called begotten or son. But the divine Word is something subsistent in the divine nature; and hence He is properly (and not metaphorically) called Son, and His principle is called Father.
The very fact that in the divine generation the form of the Begetter and Begotten is numerically the same (whereas in creatures it is not numerically, but only specifically, the same) shows that generation, and consequently paternity, is applied to God before creatures.