All perfect praise be to Allah, the Lord of the Worlds, and may His blessings and peace be upon our Prophet Muhammad and upon all of his family and his righteous companions.
Fulfilling this vow is not obligatory since, in general, the only vow that should be fulfilled is the one related to acts of devotion. In addition, fulfilling a vow to do a permissible act or leaving it according to Shafitee school of thought isn't an obligatory matter.
And the same applies on naming the aforementioned child since it is considered one of the permissible acts that fulfilling it isn't an obligation as mentioned above.
Al-Imam Ashribini(may Allah have mercy on his soul) said:" If someone vows to do a permissible act such as: Eating, sleeping or vows not to eat sweets for example then he isn't obliged to fulfill any of those vows, since the Prophet (PBUH) said “There is no vow except in an act which seeks the pleasure of Allah, the Exalted.[Narrated by Abu Dawood] Also Ibn 'Abbas (May Allah be pleased with them) reported: While the Prophet (PBUH) was delivering Khutbah (religious talk), he noticed a man who was standing, so he asked about him and was told that he was Abu Israel who had taken a vow to remain standing and not sit, or go into the shade, or speak while observing fasting. Thereupon Messenger of Allah (PBUH) said, "Tell him to speak, to go into the shade, to sit and to complete his fast".[ Al-Bukhary]" [Mughni Almuhtaj].
Therefore, you are permitted to name your child by any name. Yet, as for making a vow to fast for two consecutive months, your are free to choose whether to fast or to pay an expiation for a broken oath. And Allah knows best.
