This is not an easy request, because we do not have information on your school or what you want to accomplish through the school paper. In light of this, let me suggest a few ideas that might help.
First, since a school paper can be a little academic, you might want to consider using a Latin or Greek word. This can give it an aura of gravity.
Second, you might want to create a name based on the school's mascot or the school's motto. This will keep with the idea of school spirit.
Third, you might want something generic, by adding your school name with the word "Times, Herald, or Daily."
Finally, you might have a basket of names and have the student body vote or even have them offer their suggestions.