Changing the name of a DBA clarification

I am still confused about the process to change the name of my son's DBA.  Based on the expert responses, my understanding includes the following:

1.  For a personal income tax return (not business), Schedule C is required even if no expenses are claimed for the DBA

2.  My son has no employees.  Therefore, he does not even need to cite the DBA in Schedule C.  His social security number is sufficient.

3.  If the DBA is cited in Schedule C, the current name and TIN must be specified.

4.  To change the name of the DBA, my son must apply to the state of Texas and not a federal agency.  If so, could an expert provide the appropriate contact information.  Is a fee associated with the name change?  If yes, what is the cost?  If the cost is significant, I don't think that we will change the name.

5.  Does my son need to do anything else or know anything else in regard to changing the name.