Can you change the name on the automated emails that are triggered based on a form submission?

I have a form created where a manager will go in and enter a task and assign it to someone. I then have an automation where when a new row is added to alert the person assigned. Would it be possible for that automation to come from the manager that assigned the task via the form? Or would I need to have another button such as "send out task" checkbox where you can have that automation come from the triggering user when that button is checked? There would be multiple managers submitting so I couldn't just have them create the form.

Thanks in advance!