I for one really dislike the name "System i".
I wasn't a huge fan of the name iSeries either ... but it grew on me. At least iSeries is easy to search on. "System i" is incredibly difficult to search on ... most search engines hit on "System Integration", "System Information", etc.
iSeries was unique. If you searched on iSeries, you could reasonably expect the results to related to the system.
Of course the entire "Rebranding" thing is a pain also. How can you be touting the capabilities of a system if the name doesn't even stay the same?