All email messages you have sent will be labeled with the Gmail Sent label.

However, it is important to understand that the Gmail Sent label is not an actual label – it is a virtual label created by Gmail: all email messages sent from your account email address or from its aliases will be inside the Sent label.
So:

• It is impossible to add the Sent label to an email which is not sent by you
• It is impossible to remove the Sent label from an email message
• You cannot remove, rename or move the Sent label
• If you add an alias to your Gmail, then all email messages sent from that alias will be in the Sent label