ENS Explorer has no way to delete a .eth name: it stays registered until it expires. You can disassociate it: send it to a fresh wallet you control, with Detach the resolver on. Your wallet no longer holds the name, and the name no longer points at your wallet. To let it go for good, stop renewing it.
Good to know
Send it to a wallet you control, not someone else's, so you can move it back if you change your mind.
These steps are for a name on ENSv2: one registered on ENSv2, or upgraded to it. In ENS Explorer, a name on ENSv2 shows Roles; a name you haven't upgraded shows Fuses instead.
You need the wallet that holds the name, and the name must carry the Can Transfer role. A name in its grace period can't be transferred: renew it first.
Both wallets need a little ETH for network fees (gas): the old one for the transfer, the fresh one for the steps after it.
How to disassociate the name
Make a fresh wallet. In your wallet app, create a new wallet. It becomes the name's new owner, so keep its recovery phrase safe.
Open the name in ENS Explorer. Go to ENS Explorer, connect the wallet that holds the name, search your name and open Ownership. Select Transfer.
Enter the fresh wallet. In Recipient, enter the fresh wallet's address, and check it.
Leave Detach the resolver on. The name stops pointing to any of your records, including your ETH address. The records themselves stay on the resolver.
Approve the transactions. Select Transfer name, then Start and Open wallet, and approve each transaction. When every step is ticked, select Done.
When the transfer confirms, the Owner row shows the fresh wallet. The name's history may take a little longer to show the transfer.
After the transfer
A transfer moves ownership only: every role on the name stays where it was. From the fresh wallet, in ENS Explorer:
Remove the old wallet's roles. On the name's Roles page, check every role. For any the old wallet still holds, select the icon at the end of its row, then Remove user, Save, and approve. You need a wallet that holds Admin.
Check the subregistry, if the name has one. The name page's Subregistry row shows whether it does. First make sure the fresh wallet holds the roles you need on the registry. Then, on the registry's Roles page, remove every role given to the old wallet.
Common questions
Can I get the name back later?
Yes, if you sent it to a wallet you control. Connect that wallet and transfer the name back: see Transfer a name. If Detach the resolver was on, add the resolver back to the name and it resolves to your records again.
What happens if I stop renewing it?
Until it expires, anyone can still renew it, and a renewal keeps it with the wallet that holds it. After it expires, it has a 28-day grace period, then 21 days of Price Cooldown, when anyone can register it for an extra fee. See .eth name lifecycle.
Does this work for a name like yourname.base.eth?
No. A subname like yourname.base.eth is handled where you got it. Ask that project how to give it up.