I just use "Gasless Meta-Transactions" in https://docs.openzeppelin.com/defender/guide-metatx.
I can send the transaction with no fee when I set the name in demo App.
I'm curious that who send this transaction. Is ERC2771(smart contract) or OpenZeppelin?
Who keep the private key of "MetaTxRelayer"? Is OpenZeppelin or by myself?
The meta transaction is relayed and paid by a Defender Relay Address. Its private key lives in the AWS Key Management Service and never leaves it (it's impossible by design, not even OZ can extract them). You can manage the relayer with an API key that facilitates rotating the access.
More info in the Relay Security Consideratiomns section