Namakarana, the naming, kept small
A child's name is given on a day the family can gather. The star of the child and the tithi of the rite are both in the conversation. Neither replaces the other.
Namakarana is the naming rite. Regional days differ: the eleventh, the twelfth, a later convenient Sunday when the grandparents can travel. The child's janma nakshatra is often consulted for the sound the name should carry, in the tradition that maps syllables to mansions. That map is a custom of naming, widespread and worth following if it is your family's, and it is not a medical record.
The muhurtham of the rite is the panchang of the gathering, not a second birth chart. Do not let an app scold you for naming a child on the only day the father's train arrived. Say the name. Feed the people who came.
Pocket Pandit can score the day as NAMAKARANA. It will not propose the name. Names belong to the people who will use them every afternoon.