Listening to Spotify Music on Watch Series 3

Hello!

I have recently purchased an Apple Watch Series 3. This is my first watch with Apple, so I am not very familiar with how everything works. I have been trying to listen to my Spotify music directly from my watch, but it always plays it on my iPhone, i.e. I can control volume, pause the music on my watch, but the actual sound plays on my phone. I've tried clicking on the watch icon that allows you to select from different devices, but the watch itself is not listed in the options.

Any ideas?

Thanks in advance,

Yaroslav.