First, I just let the children name the school. This was long ago when I first started homeschooling, 2003. They loved the movie Twister and named the school Twister Academy. A couple years later, I decided to make the "lower school" Twister Academy and come up with a new name for the "upper school." I looked for names that were significant. We lived on Ellis Drive, had an Oak Tree, there was a lake at the end of the street, and so on. We considered Ellis Academy, Oakhill, Lakehill, we also thought of philosophers and such, such as Da Vinci and Socrates. In the end, we moved around this time and ended up on Lamplighter Drive so we named the upper school, Lamplighter Academy. I preferred Lamplighter School, but there is a Lamplighter School in the city and THSC said they would not print a diploma for us if we had the same exact name as another school in the state.
I hope this helps! I know of someone who used an acronym EWOK academy they were for Evangelical Warriors Of the Kingdom.