The SignUp Name is changed on the Details tab within My SignUps. Sign in, choose My SignUps, click on the SignUp and choose Manage.
The Details tab allows you to make changes to your SignUp Name, location and welcome message. The Welcome Message is visible at the top of the SignUp screen when volunteers accept an invitation to participate in your activity. Just scroll down and type in the new SignUp name:
When you are finished making changes, be sure to click the 
button before exiting the screen.