@MrsWinslow - I don't know any names for it that don't involve the word "spatula." (Except artists have a very similar tool called a palette knife.) My grandmother always called it an icing spatula.
I got by without one for years. I didn't make a lot of cakes and when I did, I just iced them with a butter knife. But my grandmother died a couple of years ago and my mom asked me to help clean out her house. In the kitchen, I found her old icing spatula, and my mom said I could keep it.
It makes such a difference! You can pick up more icing and spread it more evenly than with a puny little butter knife.