Would it be wrong to change our son's middle name?

I have twin boys that are 4. My wife got very sick during her pregnancy, and had a c-section at 28 weeks. Three days before they were born was when I found out we were having twins (my wife was in a medically induced coma at the time of birth, and for a few weeks after). Anyway we only had one name picked, and so I gave my second son's first name after my grandfather. The middle name was picked by my wife's best friend/sister, but she doesn't like it. She signed off on the names when she was concious, but she says she never got the chance to put thought into it. She would like to change his middle name into something more meaningful to our family. Do you think this would really effect our son if his first name stays the same? Or do you think its better if we just add a second middle name? It really bothers my wife. What do you think?