Nāmākhilasya vyavahārahētuḥ, śubhāvahaṃ karma subhāgyahētuḥ| Nāṃnaiva kīrtiṃ labhatē manuṣyaḥ, tataḥ praśataṃ khalu nāmakarma||
Nāmakaraṇaṃ, is the saṃskāra in which the parents or the father gives a name to the newborn child. The name of the saṃskāraḥ also means the same. The primary purpose of giving a name is to call him with it for better communication. According to the tradition, giving a good name to the child would give him good fortune. A name could also help in becoming famous.
jananāddaṣarātre ṣatarātre saṃvatsare vā nāmakaraṇaṃ 
yadvā piturabhāve ayogyatvamathāpi vāǀ anyo vā kulavṛddho vā jātakarmādi kārayetǁ 
In Indian tradition, a child is generally named after their Kuladēvatā/ Household god, Ancestors or Āchāryaḥ/ Teacher. The name can also be chosen according to Jyōtiṣhyaṃ/ Astrology. According to the birth time, date and place some letters are prescribed at the starting and ending. This saṃskāraḥ is performed according to one's tradition, which may differ from household to household. In the Dharma śāstraṃ, many days were suggested to perform Nāmakaraṇaṃ. Like on the 10th or 11th or 21st or 100th day from the birth. Father is considered to be the main performer, but if the child's father is dead or not available by any other reason, it is instructed that anyone or any elder of the house should perform nāmakaraṇam.
After nāmakaraṇam, there is a small saṁskāra called as karṇavedha. Karṇavedha means piercing the ears. The ears are normally pierced by a sharp golden wire, which appears to be an ornament. It is advised to perform the saṁskāra before the new born gets his/her first teeth. It is advised to perform the saṁskāra on an auspicious day in the lunar month of kārtīka, puṣya, chaitra, and phālguna, that too in the śukla pakṣa.
kārtike pouṣa māse vā chaitre vā phālgunepivāǀ karṇavedhaṁ praśaṁsanti śukle pakṣe śubhe dineǁ
śiśorajātadantasya māturutsaṁgasarpiṇaḥǀ sauciko vedhayet karṇau sūchyā dviguṇasūtrayāǁ
After nāmakaraṇam, there is one small saṁskāra called as 'niṣkramaṇam'. Niṣkramaṇam means coming out. In the present context bringing the newborn child from the place of his/her birth is called as niṣkramaṇam. This saṃskāra is instructed to be performed on the twelfth day, third or fourth month after the birth. On this day the child should be shown to the Sun and the Moon.
niṣkrmaṇam candra-sūryadevatādarśanaṁ ca dvādaśehani tṛtīye chaturthe vā māsi kuryāt. 
- Vīramitrōdayaṃ by Bṛhaspatiḥ
- nāmnaḥ karaṇaṃ, assigning a name
- bahvṛca pariśiṣṭa, smṛti muktāphalaṁ, p.81
- smṛti ratnaṁ, smṛti muktāphalaṁ, p.81
- sāyaṇīya, smrti muktāphalaṁ, p.82
- smṛtyarthasāraḥ, smṛti muktāphalaṁ, p.82