Looks like you are from Texas, so your questions fall under the jurisdiction of the Secretary of State.
If corporations, limited liability companies or limited partnerships (entities created by filing with the secretary of state) do business with a name that is different than the name set forth in the organizational documents, they must file assumed name certificates in the county or counties where the registered office and the principal office are located, and must also file with the secretary of state.
Here's the link to their home page:
www.sos.state.tx.us/index.html
As Mum24kids indicated, it would be unusual for your PTO to be using something other than its official name, in which case you need to do nothing beyond the normal steps. But if you ARE indeed using a different name, then the above applies.
And note (in Texas)unlike a business corporation, it is not necessary for a non-profit corporation to use one of the corporate endings (Corporation, Company, or Incorporated).