To be precise:
- the stake address registration fee (2 ADA) is per owner account. So if you have multi-owner or a separate reward account, you would need to multiple that number accordingly.
- you would also need to pay transaction fee (which is around 0.17) when register/publish the pool. You may need to perform multiple transactions if you like to update parameters or correct mistakes.
- Like others pointed out, the 340 ADA is not part of initial cost.
Also note both 500 ADA pool deposit and 2 ADA key registration are refundable.