The sender name is shown next to your email address in mail clients like Gmail or Outlook when you send an email using Email for Trello.
Setting the 'Sender Name' in Email for Trello
You can change it by editing the SendBoard Power-Up settings, which you can access through the Trello sidebar. Click on the SendBoard button and choose "Edit Power-up Settings".
Go to the "Mailbox" tab of the SendBoard settings and update your Sender Name.