The preferred way to refer to the region, and not the river, depends on the specific subject you want to talk about. Is it the Amazon basin? Is it the Amazon forest? Amazonia is also an option (two references below). However, all are gramatically correct.
Patrick Lavelle et al. 2016, from France, published on 'Global Environmental Change':
Michael J. Lathuillière1 et al., 2016, from Canada, published on 'Hydrology and Earth System Sciences':
Some more considerations:
I'm being more subjective here, but 'Amazonia' sounds broader than 'the Amazon'. No one will question you are referring to the forest in the first case, but the second case may take a little more brain processing, because the word 'Amazon' can refer to so many other things.