If you use anything other than Amazon's in-house streaming service Amazon Music, you should take a few seconds to change the default music streaming service.
To do this, open the Alexa app, then go to More > Settings > Music & Podcasts > Default Services. Select Select your preferred streaming service under the Music, Artist and Genre Stations, and Podcasts banners.
Now when you play music, you won't have to specify what service you want to stream it. However, if you still want to use Prime Music or Amazon Music Unlimited, at any point you can say, "Alexa, play [song or artist] on Amazon Music."