In English, we say fifteen hundred. Similarly, for 1590, we would say fifteen ninety.
It is correct to say "in the year one thousand five hundred", but uncommon and used for emphasis/dramatic reasons.
For example, when one says that "Columbus discovered America in 1492", one would usually say "Columbus discovered America in fourteen ninety-two". However, one could also say "in the year one thousand, four hundred and ninety two, Columbus discovered America". This is more dramatic, but is unusual - something you might hear a narrator say in a documentary about Columbus, but not something you would hear in day-to-day conversation..
Meanwhile, for the year 2000, we say two thousand, not twenty hundred. But for 2016, we say twenty sixteen.