Can a parent name a trustee if there was no will

In the event of a death without a will, you can request to be appointed as the administrator of his estate.  There are certain person who have "priority" to serve as administrator.  they are all biological relations to the decedent.  If they renouce their priority in favor of you, you can be appointed.  You can also file a petition with the court to be appointed and those people will receive notice and opportunity to object.  If they do not, you can serve.  Whatever is statutorily left to your son via the laws of intestate succession will have to be paid to a court appointed guardian for his benefit until he reaches the age of majority.  This process is complicated and I would suggest that you retain counsel to assist you.