Our ancients, it would seem, attached great importance to naming of a child. There is voluminous material available on the subject. To condense it all is a very difficult proposition. What is being attempted here is to give a gist of divergent views of various authorties. Only the major authorities are being referred to and what are presented are only major points.

When a male child was born, it was given atleast two names, one an ordinary one and another a secret one, known only to parents and used till the boy goes through the Upanayana ceremony. A third name was given later in life which signified the achievement of the individual during later life. Generally three names are mentioned in vedic literature, an ordinary name, a name derived from the father and a gotra name ( or a name derived from a remote ancestor).

Brahadaranyaka Upanishad, Asvalayana Griyha Sutra, Sankhayana Grihya sutra and Kathaka Grihya sutra speak of giving a name to a child on the day of its birth.

Apasthamba Grihya sutra,Bharadvaja Grihya sutra and Paraskara Grihya sutra, it is said, mention that the 10th day after the child is born is the day of Namakarana. Some authorities mention that it should be done on the 11th or 12th day. It is said that Gobhila and Khadira Grihya sutras mention that any day after ten nights, one hundred nights or a year from birth can be the day of Namakarana.

The following points find a mention:
The name should begin with a sonant and contain in the middle a semivowel
The names of male children should contain two or four sullables or an even number.
Some sutras prescribe that the name should end in a visarga preceded by a long vowel.
The name should have two parts, the first being a noun and the second being a verbal formation(generally a past passive participle).
The name should have the upasarga ‘su’.(such as Sujata, Sudarsana, etc).
The name may be derived from a sage or deity or ancestor.
There should be a general name and another Abhivadaneeya name, known only to the parents till Upanayana and used by the boy to announce himself in respectful situations.

As for girls special rules find a mention:
The names should contain an uneven number of syllables. Manava Grihya sutra, it is mentioned, says that the name should be of three syllables.
The name should end with ‘da’.(such as satyada, Vasuda, etc).
Some authorities say that the name should end with an’I’.
Some others say that it should end with a long vowel.

The general rules are that the name should be easy to pronounce, should not suggest any harsh acts, should be pleasing to the ear and should convey some blessing..

It is interesting to note that the Asvalayana Grihya Sutra does not mention the samskara of namakarana at all.

Some Grihya sutras prescribe that the Sutagni should be removed and homa for namakarana should be performed in the Aupasana fire. Bharadvaja Grihya Sutra, it is said, prescribes chanting of Jaya, Abhyatana and Rashtrabhrt mantras and offering of 8 oblations of clarified butter. Hiranyakesi Grihya Sutra prescribes offering of 12 oblations and giving two names, one ordinary and another a secret name..

Medival works that comment on Dharma sastras and jyotisha mention ways of deriving names from nakshatras. Each of the 27 nakshatras are divided into four padas and to each pada a specific letter is assigned. For instance for the four padas of the star Aswini, the letters are ‘cu’, ‘ce’, ‘co’, and ‘la’. The names derived can be for example, Cudamani, Cedika, Colesa and Lakshmana. These names are secret and are wispered into the ear of the brahmachari at the time of his upanayana. The names are used in abhivadana, chanted during performance of pratha, madhyanhika and sayam sandhya vandanam.

As mentioned earlier, there is a lot of material available and all of it cannot be condensed for the simple reason that there is great divergence in the views of the various authorites.
The practices also appear to have undergone modification during the passage of time.

Present generations are not bothered about rules and regulations. They are happy as long as the name sounds fine.