I would recommend naming the child "Belenus." That way, you can still use the name "Bile" as a nickname, and you can change the spelling if you ever move to an English-speaking country.
These other comments are all very ignorant. You are only seeing things from the perspective of the English language and culture. Please have some respect for Celtic culture. The name Bile stems from Irish folklore and Celtic mythology. Look at this name from a different perspective, and it will make much more sense.
It is the Irish variant of Belenus, a sun god, and the the Welsh Beli. Belenus and Beli stem from "Bel-" meaning "light" and "shining one"/ "fair shining one."
In Irish mythology, Bile is the Irish god of light and healing. In Irish Gaelic, the name translates to "sacred tree". All three variations of the name are also related to the Beltaine. Beltaine, meaning "bright"/ "brilliant fire", was a fire festival to honor Bile. It marked the beginning of summer and the growing season, and symbolized rebirth and the return of life to the world.