Each pool has its own way of identifying you on their platform - it can either use anonymous mining or it can support mining through registration. In anonymous mining it usually identifies you through your wallet address while on mining through registration you get identified with your username or mining account name that you need to create on the pool's dashboard.
Anonymous mining is a mining process where the only mandatory information to provide to the pool is a wallet address.
Anonymous mining is more common than mining through registration, with pools like Ethermine, 2miners, Ezil.me, and Nanopool being some of the well-known examples of such pools.
You need to create a wallet address on the correct blockchain and network (i.e. for Ethereum, the network is ERC20), add the wallet address in the address editor, select it in the miner configuration. Pools will authorize you based on the address you're using and send to the provided address the amount of cryptocurrency you've mined (authorizing with that address) once you reach the minimum payout threshold.
Contrary to anonymous mining, and as leads from the name, this method requires you to register first, most often with an email verification too. While it requires more effort, this method is considered to be more secure and convenient by some users.
The exact way the pool operates varies from pool to pool, but a common trait is ability (and necessity in some cases) to create mining sub-accounts, which you add as wallet in the address editor and select it in the miner configuration so that the miner is able to authorize on the pool to indicate that it's indeed you who's mining.
With sub-accounts you can mine to the same wallet using not only different rigs, but different sub-accounts, which you could use to indicate different mining locations.
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