Recently, several of us have been challenged by a few people who claim their Y-DNA infallibly "proves" their direct male line back to a specific person (usually their 5th or 6th great-grandfather or, sometimes, even further back). When confronted with documentary evidence debunking their claim, they respond with something along the lines of "Nope, Y-DNA trumps all." Well, guess what folks? Your DNA may have a wealth of information about you-such as genetic codes for your stunning-good looks, your hazel eyes, your crooked little finger, etc. But it does NOT have genetic codes for names--not your name, not your dog's name, not your ancestors' names, not any names. So, what does your DNA prove or not prove? And, how did these misguided folks think DNA came up with their ancestor's name?
To answer the first question, let's just stick to what's of most interest to genealogists. Your DNA testing company will give you a list of your DNA matches. These are other people who have taken the same test and whose DNA closely matches yours. Is it a 100% match? Not at all, even identical twins don't have 100% matching DNA. Your matching person is probably your relative although there's a small chance he/she is not related to you at all. There are several reasons why your match might not be related. First of all, testing companies don't test your full DNA, they only test those areas that are most likely to differentiate you from other people but not even all the possible areas where differences might show up. So, it could be just pure coincidence that you match on the areas tested but mismatch on untested areas. Then, there's a chance the samples were contaminated. And finally, there could have been a mix up in the lab. The probability of a false match is low for your closest matches but rises exponentially for your more distant matches. AncestryDNA gives only a 15% to 50% confidence overall for matches that they predict are your 5th through 8th cousin. Family tree DNA won't really give you the probability of a mismatch but they kinda dance around the issue by stating that if you match all 67 markers on a Y-67 test AND YOU AND YOUR MATCH HAVE THE SAME SURNAME, then there's a 90% chance that you and your match share a common ancestor within the last 5 generations. They follow this up by stating "Very few people achieve this close level of a match". Yeah, fine; so, what's the probability of a false match? They don't tell you.
OK, so DNA tells you that you and your match are related (maybe). And. if you are maybe-related, then you will--maybe--have a common ancestor. But the DNA cannot tell you exactly how many generations back that ancestor lived. And, most certainly the DNA cannot give your maybe-ancestor a name.
Which brings us to question two: if not DNA then where did the ancestor name come from? The truth is that it came from the family tree of someone whose DNA sortta matches yours. Yikes! A family tree? If you are anything but the newest genealogy buff, you have probably complained about how many family trees at the major sites like Ancestry.com, myheritage.com, etc. show conflicting information when going back five or more generations. You have to ask yourself how much do you trust the tree of your DNA match? Did he/she do exhaustive research or did he/she just copy from someone else who might have been a complete idiot. It all boils down to this: DNA can lead you to someone who might be distant relative who might (or might not) have proof of his/her ancestry. It's up to you to determine if your DNA matches really know what they're talking about or if they have a faulty tree that was just copied from someone, who copied from someone, who copied from someone... who copied from someone who was just guessing (and was a bad guesser at that).
So, does Y-DNA infallibly prove your ancestor's name? No way! At best, DNA can lead you to people who might know. But actual proof only comes from traditional genealogy methods and evidence analysis along the lines of the Genealogical Proof Standard as published by the Board for Certification of Genealogists. If your DNA match has done his/her homework AND can show you the proof, then whoopee! DNA led you someone who had the answer but the answer was in their tree. not in the DNA itself.