We did rename our daughter though only slightly... her Russian name was Yulia and we "Americanized" it to Julia. We also changed the middle and (obviously) the last name too. Our daughter was named by a nurse at the hospital (as someone mentioned earlier) but did receive the last name of the birth mother.
I really think it's a personal choice, but if you would like to change it, there shouldn't be anything stopping you from doing it. In some cases, the kids want to "fit in" and often times a new name does that.
Just my opinion though...
