What is the name of Amazon's streaming media player?

Amazon's streaming media player line is called Fire TV.

Amazon announced the first Fire TV on April 2, 2014, and made it available in the United States for $99. The compact set-top box connected to a television through HDMI and streamed video and music over the internet. It also supported apps, voice search through its Bluetooth remote, and a selection of games.

The Fire TV family later expanded beyond the original box. The Fire TV Stick offered a smaller HDMI-connected design, while the Fire TV Cube combined streaming hardware with hands-free Alexa features. Amazon also licensed Fire TV software for smart televisions made by other manufacturers, so Fire TV can refer both to hardware and to the television platform.

Chromecast, Roku, and Apple TV are competing streaming products or platforms, not Amazon's own name. Another common mix-up is Prime Video: Prime Video is a streaming service, whereas Fire TV is the device and software ecosystem used to access Prime Video and other services such as Netflix, Hulu, and YouTube.