All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

Executing the vow to name that child "Islam" isn`t obligatory because it is lawful to give him that name, and a Muslim isn`t obliged to execute a vow that concerns a lawful matter, so he/she is to decide, and this has been clarified in our Fatwa No.(245).

Moreover, you (asker) aren`t obliged to execute your father`s-in-law wish to name your child "Omar" since, from the perspective of Sharia, the will that should be executed is the one involving wealth and not that concerning what is lawful or recommended.

Defining a will, Al-Khateeb Ash-Shirbini said: "It is delayed delivery of a possession till after someone`s death" {Moghni Al-Mohtajj, vol.4/pp.66}.

In conclusion, you are free to choose any name to your child as long as it is lawful and good. And Allah Knows Best.