If you have had much contact with priests over the past fifty years you must have heard a priest say "Just call me 'Joe'" (or whatever his baptismal name is), by way of humility, simplicity and being "more personal" and "with the people." Now there is a generation of priests who want everyone to call them "Father" including their natural parents and their priestly comrades. My experience of both trends is that the men who rejected the title tended to be lax and disoriented in many other areas of their priestly call and identity whereas the new men have a clear notion of the priestly dignity as a ministry of sacramental service and fidelity to the Church.
The title "Father" is actually more supernatural, and therefore humbler, and more intimate. It is more supernatural because it is given by the bishop who ordains the priest whereas the baptismal name is given by the priest who baptizes. "Father" is a reference to the representational nature of the priesthood, that the priest is God's representative, and that that representation is not primarily a matter of function but of essence: he "is" a priest. That is "who" he is, not just what he does. If he continues to be "Joe", than where is the change? And that change is the same regarding even his natural parents and his brother priests. All should feel honored to acknowledge the reality of the sacrament in the ordained minister by always using his title. It is a confession of faith in God. This is particularly striking with some Hispanic children who will endearingly call the priest "Papa Dios" (Daddy God). Priests represent God!