I don't know how it will affect your GC, but I had

the same problem for my I-20 too. My name should be Jingtao XXX, but somehow my advisor put my name is this way: Jing Tao XXX. Finally my name became Jing Tao, and my family name became Tao in my I-20 and all other applications in the University. Upon my graduation, graduate school could not find my name Jingtao XXX. They told I could not graduate because no record for Jingtao Wang. In short, lots of trouble because of the name.