Sometimes testing the Y chromosome can help when you are looking for a missing father, grandfather, or further back as long as you have a tester descended on the male only line. Remember the Y is passed father to son, so any changes are rare and are caused by mutations not recombination. Typically a man would start with a Y 37 STR marker test at Family Tree DNA to see if this avenue is worth pursuing. A STR test gets the most recent changes rather than the haplogroup, thus can suggest a surname. Click here for my article explaining Y testing.
The Y results will not help if no other men from that Y lineage have tested unless you have a theory. In that case you need to test someone else descended on the male only line from the presumed ancestor.
Y testing can be very useful when the unknown parentage occured many generations ago, such that autosomal testing may not be able to solve it.
If your ancestors have been in the USA for some time then a Y 37 STR marker test may find a probable last name. In that case there may be a surname project with other Y testers at Family Tree DNA. I recommend contacting the admins of that project as they can often be a great help in your quest. However if you are from a population group which has only had inherited surnames for two hundred years or less, quite likely you will have no luck.