Looks marginally less offensive in the video than in the pictures. Maybe that is because the camera was moving further away?
So far as naming it is concerned, it all comes down to manufacturers getting away with as much as they can. Fiat obviously want the 500 to rub off on everything they sell, because the 500 is popular and fashionable (unlike the rest of their offerings). My local free newspaper ran a piece on the 500L when it was announced which was a mildly regurgitated version of Fiat's press release. If the car was called the Fiat Testa di Cazzo (or something) then I strongly suspect that the Herts Advertiser would not have picked up on it and would not have printed its glowing words and the official Fiat photograph.
So for Fiat, so long as calling it a 500L is not expected to spoil things for the 500, they are bound to call it the 500L and hope that the 90% of car buyers who know nothing about cars and get their car buying advice from the Herts Ad (and similar) rather than Maxi or Max Power, swallow the spiel and buy into the 500 dream.