The ERC1155 contract name and symbol will automatically appear on Etherscan if you declare these two variables as public in your contract. See the ERC1155 code sample below.
Inside your contract constructor, you should then assign your contract name and symbol to values that represent your contract. Once you assigned them and deployed your contract, this text will appear on Etherscan automatically, as illustrated below by Adidas ERC1155 contract.
All of the above is automatically done for you when you create an ERC1155 contract with Mintnite.