All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
To make a vow to name the child with a particular name is a permissible vow and the scholars differed with regard to the ruling of fulfilling such a vow. The majority of the scholars are of the view that it is not an obligation to fulfil such a vow. However, the Hanbali school is of the view that it should be fulfilled and the person who made the vow has the choice either to fulfil it, or to expiate for the vow. It is better to opt for this last opinion.
Therefore, there is no harm on this person in not fulfilling the vow but it is better for him to expiate for breaking the vow. For details on the expiation, please refer to Fatwa 102811.
Finally, it should be noted that such a vow that is conditioned on the occurrence of something is disliked. Al-Bukhari and Muslim reported that the Prophet warned against vowing and said that it only extracts something from the stingy people.
Allaah Knows best.