When should a baby be given its name?

Shaikh Bakr Abu Zayd (rahimahullāh) said:

There are three times reported in the Sunnah from the Prophet (salallāhu ʿalaihi wasallam) wherein the child can be named:

1. Naming the baby on the day of its birth.
2. Naming the baby on the third day after its birth.
3. Naming the baby on the seventh day.

These are variational differences (ikhtilāf tanawwuʿ) that show the matter is open [to one’s choice] – and all praise is due to Allah, Lord of the worlds.

(Tasmiyat al-Mawlood, p. 28)