Hi Raymond, The Ancestry test you took is an autosomal test (auDNA). When you match someone else's DNA you can tell approximately how far back the relationship might be by looking at how much shared auDNA you have. yDNA is a bit different. Women do not have a y Chromosome and only men can take a yDNA test. If your yDNA test shows that you match another man fairly closely (35, 36 or 37 markers out of 37) then you can be fairly certain that you share a paternal line ancestor (father/grandfather/great grandfather, etc) in a genealogical time frame. (It is valuable many generations further back than auDNA.) Because in our culture children generally take the surname of the father, IF you have a number of matches with men who all have the same surname, you will probably know the surname of your father. I wrote IF in capital letters intentionally. For various members of my family I have worked with these surnames: Smith, Wilson, and Stone. For Smith and Stone my male relatives had 10 or 12 matches each with the same surname, and the yDNA has been very helpful in working on tracking down the male line. My Wilson relative doesn't have any close yDNA matches and the more distant ones all have different surnames, not Wilson. As with any DNA test, it depends on whether or not other people related to you have also tested. So it's a bit of a long shot. It has a lot of potential for you if a male relative of your biological father has tested.
You wrote that you have uploaded your DNA test to GEDMatch.com. I recommend that you put your GEDMatch ID on your WikiTree profile. Do you have any close matches there? If you do, that could save you the expense of a yDNA test.