Is my web3name automatically linked to my KILT address?
No, your web3name is connected to the decentralized identifier (DID) you generated when creating your Sporran account and not to your address. Linking to an address needs another step.
There are two different ways of linking addresses to a web3name, with two different functions:
Using w3ndi, for sending and receiving funds from multiple chains via a web3name
Using account linking, to link multiple addresses across the Polkadot and Ethereum ecosystems to a DID (and its associated web3name, credentials, and service endpoints).
Note - don’t link addresses that you don’t want connected to your name! If you want to keep an address private, don’t link it.