Let's say for example I bought pokebank with an account I named as 'NoobMaster69' on 3ds 1. I buy another 3ds for whatever reason and I want to use the pokebank on 3ds 2. So, can I use the pokebank I bought on NoobMaster69 on 3ds 2?
The Pokémon Bank account that a Nintendo 3DS system accesses depends on the system's Nintendo Network ID, which can only belong to one Nintendo 3DS system at a time.
I believe this means no.
Source
Hope I helped!