mads9999,
Your employer can change name - all that will be needed will be a declaration stating that name of the company has changed - your Lawyer will have to take care of it. it will not have any impact on your application at any stage.
But ensure that it is only change of name and not that they are closing one company and opening another and telling you a change in name.
I know one company in NJ, which told its employees that it is a change of name and behind the scene-closed the old company(as they had problems with INS.). One of my friend, working for the same, was alarmed only when they reapplied for his H1 on the pretext that they would like everyone to have new name on his/her document and they are kind enough to 'invest' for convinience of employees. He hit them back by joining his client, as the original company was there no more - so he was not bound by any agreement any more. It was easy in his case to find out as his Previous company was registered in name of his employer's wife and later one in his employer's own name.