Allah's Messenger (sallallahu alaihe wa-sallam) said: "Every child is held in pledge for his Aqeeqah which is sacrificed for him on his seventh day, and he is named on it and his head is shaved." [(Saheeh) by Shaikh al-Albanee (1165) Abu Dawood (vol: 2, no: 2831) and others]
Another narration in this aspect is related by Anas (radhiallahu anhu), who said: 'Allah's Messenger (sallallahu alaihe wa-sallam) said: "A boy was born to me this night and I have given him the name of my forefather Ibraheem." [Saheeh Muslim (4/ 5733)]
Anas Ibn Malik (radhiallahu anhu) narrates in a long Hadeeth that Allah's Messenger (sallallahu alaihe wa-sallam) named the son of Abu Talha, he said: The Prophet took a date, chewed it, took some of it out of his mouth, put it into the child's mouth and did Tahnik for him with that, and named him Abdullah." [Saheeh al-Bukharee (7/379)]
In light of these Ahaadeeth we understand that the child can be named on the first day of his birth or it can be delayed until the seventh day. However, what is recommended is to name the child on the seventh day, as such is related in the saying of Allah's Messenger r. Regarding the Hadeeth which mentions the Prophet's practice is taken as an evidence to prove that the child can be named before the seventh day.