There is no option for inputting description in ethereum blockchain transaction, below is the transfer steps in MEW web wallet, the only space for inputs are.

Typeoftoken>>amount>>toaddress>>transactionfee>>advanced

Same thing above happened in trust wallet transfer steps, there is absolutely no space for description or label your transaction. It goes..

Recipientaddress>>amountETH>>networkfee

Beside, having a description on a transaction can only be done on some cryptocurrency exchange, example of such exchange is huobi, this exchange supports an option to have a little write up about your transaction, note that the description is excluded from the blockchain. However the only signed message that's included in ethereum blockchain is the cryptographic message sent from the owner to the contract

Regarding the signed message, in ethereum network, you can sign a message by showing some proof ownership of wallet, therefore, it involves using a private key in the process, you can read more here in how to sign a message in ethereum blockchain if that's what you truly want, how to sign a message?