If my father died last year and he had stocks is his name only, how can my mother change the name on his stocks?

I am so sorry for your loss.  If the stocks were in his name only then they are part of his estate.  Since he died with out a Will - called intestate - the intestacy laws in the state will govern the distributuon of his assets.  You need to get some help here.  Start by finding out the value of the stocks and see if they qualify for a small estate proceeding.  I am assuming that everything else passed to your mother though joint ownership at the time of your father's death.  But they are going to have to go through probate.  Good luck.