Muhurth is fixed in 2 steps shown as 2 rules tables below.

1. Find the days suitable in a month.  Select the day. This is based on Month, Day, Nakshatra, Tithi, Yoga, and Karana. 
2. Find the time of the event. This is based on the horoscope of that moment. What is rising ? What is setting or going to set ? etc.

Namkaran. This Sanskar is performed on the tenth , eleventh or twelfth day after birth, with recitation of Mantras. The baby child gets name on completion of this Sanskar. The first male child is usually named after his paternal grandfather, the second male child after maternal grandfather. The first female child is usually named after paternal grandmother and the second female child after maternal grandmother. The rest of the children carry names of uncles, aunts, gods and goddesses. (naming ceremony) life and glory are improved and an independent existence comes into being.  While good music like bell tinkling is on, whisper name of the child in its right ear.