Ever since FIAT took over Alfa, they have been offending enthusiasts by selling them badly built, unreliable cars that depreciate like a stone. So no change then.
Pedant point: Fiat (mixed case) has been the company name for donkey's ears. Wikipedia and many derivative articles place the name change in 1906. A quick peek at Pomeroy's Grand Prix Vol 1 suggests F.I.A.T. for the 1906 French GP and Fiat for 1907, although Pomeroy also uses F.I.A.T. when referring to later cars...
Grace's Guide (http://www.gracesgui....uk/Fiat_Motors) provides some fascinating adverts for Fiats, F.I.A.T.s and FIATs, which suggest that the UK importers were confused too for many years.
Body and radiator badges throw up further confusion. It is easy to find photos of Fiat radiator badges on authentic pre-1906 cars, when the company name was most definitely F.I.A.T. More common Fiats of later times are badged FIAT.
Today the holding company is Fiat Chrysler Automobiles, a successor to Fiat S.p.a which was commonly known as Fiat Group.
FIAT has not been ALL CAPS for a long time. Perhaps a contributor with access to Italian company records might chip in. However we have to consider that importers may not have changed business registrations at the same time.