It's trying to be a (giant) 500 for starters. It;s trying to be "cool" by doing so.
I don't think the grande was cashing in on the punto name, for starters the punto name wasn't "cool" or "fashionable". It was Fiats car for the segment, the Grande replaced it in that segment. Yes it was bigger, but they at least made the name fit.
The 500 name is because it became a fashion brand.
The 500, historically is a cheap, basic city car. The remake is not cheap, or basic for that matter, but the fact it harks back to the original looks wise and by todays standards of huge cars is now a small car too, so makes it fine. Then cashing in on the success by making a range of 500's that have bugger all to to with the 500 in either looks (grafting a face onto anything does not count), size or philosophy is a sell out of the Fiat 500 name.
The 500 name, because of the fashion aspect made Fiat think "we'll slap it on everything and it will hopefully sell to the fashion conscious side of the market still
What next, the Fiat rival to the 6 wheeled Merc G Wagon? The 500VI? Maybe a double decker version to rival the Routmaster? The 500DD? They could even do a special edition where all the seats have cupholders and call it the 500 Double D cup
They'd all have as much to do with the 500 name as the 500X or 500L (which should have been called the 600 Multipla, and yes i will forever be sore about that being a traditionalist
)