Can the PTO use a schools name without the permission of the Principal?

I'm not a lawyer, but I would say as long as a group is not representing themselves as the school, there should not be a problem. In any case, the principal does not own the school-if anyone were needed to giver permission, I would think it would be the school board. But I don't even think that is necessary. If this is a private school, there might be an issue.

Anyone else have any actual insight?

Its owned by the parents and stakeholders via taxes, etc. The principal has no claim or right to not let them use the name, that I know of.

It would be hard to be Anytown PTA/PTO without Anytown Elemnetary in the title, wouldnt it?

'PTA/PTO Elementary School in our neighboorhood' sounds just as bad as the 'Los Angeles Angels of Anaheim'

I actually have a insight to this, our group has our school name in it and we did not have to get permission but our principal started the group. HOWEVER when we went to incorporate in NY we had to have letters from our district stating we could use the school name and approval from the NY state department of Education before we could use the name to file.