No one will pronounce it right. Everyone will pronounce it Jay-mee instead of Hi-mee. Not to mention youll be cursing your son to a life of strange looks and demands for explainations and a lot of teasing and maybe even bullying.
That's one of my many first names: Jaime, James , Jim, Diego, Jacques, Giacomo, Dimitri, Tiago, Jimmie, Jimmy, "JT" ( middle name is Thomas), and more that I can't think of right now: and I'm French and Irish - Hispanic friends call me Diego, Latino friends call me Jimmie, Italian friends call me Giacomo, French friends call me Jacques, a Russian friend calls me Dimitri, Brazilian friends call me Tiago, Americans and some Europeans call me Jim or James - one name, many translations.
What does the name Jamie have to do with being Hispanic? It's a nickname for James, and is of Scottish/English in origin. Understanding that there is a Spanish/Portugues version as well, however it's pronounced very differently. So if your not Hispanic, then it's not like anyone is really going to think anything of it. But really you can name your child whatever you want to.