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. Linking the name and DIDaddress to any of your addresses requires an extra step - see the instructions on the web3name Promo website or follow the guide here.

NB - 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.