Sayyidina Aby Musa Al-Ashari (R.A.) said:
"When my wife deleivered a baby boy I took him to the Prophet (S.A.W.). He gave him the name Ibrahim and chewed a date whose juice he placed on the palate of the child. He made a supplication for his welfare and returned him to me. This was my first child." (Bukhari).

Sayyidina Anas Ibn Maalik (R.A.) narrated that when Abdullah Ibn Abu Talha was born he took him to the Prophet (S.A.W). He has a gown over him and was applying ointment to his camel. On seeing the child, he asked Anas if he had a piece of date with him and he confirmed that he had and presented a few pieces to him. The Prophet (S.A.W.) chewed a piece of those dates and applied his saliva to the child's palate who seemed to enjoy the taste. When he observed the child's pleasure, the Prophet (S.A.W.) remarked. "How much do the Ansar like dates!" He then named the child Abdullah.

Sayyidina Asma (R.A.) said:
I was pregnant with Abdullah Ibn Zubayr when I left Makkah for Madina. I was already experiencing the pangs of the child birth and i stopped during the journey at a place where Abdullah was born. I took him to the Prophet (S.A.W.) who asked for dates to be brought to him and after chewing one, he applied to Abdullah's palate the saliva from his mouth. The first thing that went into the child's mouth was the Prophet's saliva. He then prayed for the well-being of the child and named him Abdullah. He was the first Muslim child to be born at Madinah after Hijrah and everyone expressed happiness at that, for, they heard that the Jews had claimed to have performed sorcery against the Muslims so that they would never have a child. (Muslim).

 From the above examples it can be seen that dates should be eaten and small amount of juice should be given to the child too at birth and naming. It is also recommended that a Dua of well-being should be made.