Look for things that are important. Like maybe heritage or something. Ours is our last name hill academy. We added hill because it is mostly family that lives in the area has been called that too. Since we used our last name I wove that heritage into it. It will come to you. It took me a year to get ours all figured out.
Ours is our last name plus "Academy" but I think I need to change it. It will look odd on her high school diploma, I think. Not that I want to hide that she was homeschooled, but I do think we need something a little more formal.