I dont think it will affect in anyway as long as you are doing the same job..Here's my experience..
I applied for RIR on August 2000 and got it approved December 2000..(ya 4months...my luckiest moment in life)..In Jan 2001, our company got bought over, but still our whole entity didn't change..reporting to the same 100 bosses above me...doing the same work..attorney said don't worry nothing will get affected with this..In Dec 2001, then we merged with another company..and sometime in 2002 our company name changed..then again in later 2002 and then again in early 2003.
But all these years, I am still working in the same group...with the same title (actually I was promoted later)..to the same 100 bosses and our division name has never changed either..
Anyway, that's my knowledge of it..donno if I am right or wrong..but I guess the attorney should be right..
Hope that helps
Madhav