You could put different squares together of primary colors and then have make handprints to put in each one. If you don't like applique, you could draw handprints in each square and print each child's name in.
You could also get a hold of the principal and explain what you want to do. They are much more forth coming with just first names on a project like that.
Maybe applique'd apples instead of handprints with the kids names on them.
There are tons of options