You only need one account, but your music will only play on one dot at a time.
If you want the same music on both for any reason, you are out of luck. It will only play on one at a time, unless you have 2 Amazon accounts and the music will be different on each with separate accounts.
There are a couple of oddities I've seen people express issues with, such as asking for music when near one dot, and the music plays from the other dot...
Evidently you need to be a millionaire to get full home music coverage with the Amazon systems, by purchasing a house full of Sonos Branded home audio speaker systems...