The fact that the 'established' team changed names again certainly suggests it could easily have been The Crows rather than Giants or Bite.If we were creating an ABL team from scratch than I’d be all for calling them the Crows (ala GWS and Collingwood in the netball).
The difference with the Giants (or Bite at the time of acquisition) is that they were already an established franchise. To rebadge them as the Crows would not only crap all over the heritage of the Bite/Giants, but would alienate the Bite/Giants fans that aren’t Crows fans.
The Thunderbirds learnt this the hard way when Port sponsored them in the late 2000’s - a misstep they still haven’t fully recovered from.
The Thunderbirds made a mistake in that it was a temporary sponsorship arrangement. You should not change your name for something like that. If it was purchased and became a permanent change it is not such a big deal.