I homeschool my 3 children that ranges from elementary to highschool. When we were deciding on a name we chose to go with where we lived...Dry Branch Rd....and then went with academy because of the wide range of grades we are doing so we have Dry Branch Academy. We think it sounds so official :).
Maybe you could start with a significant name...such as family last name, favorite historical or biblical figure, or where you live and then attach school, academy, etc.
M.H.