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Oops! I had re-cropped the image so the last bit wasn't cut off but posted the wrong one. Here's a close-up.

Thank you for the help.

Quote from: rlw254 on Saturday 30 May 20 17:45 BST (UK)

There's a difference between using Y-DNA testing to find close paternal matches and using this type of test to determine a paternal surname. The former is much harder and, as people have said, can require a long-term investment and some luck. If, however, you just want to determine a paternal surname, a Y-DNA test can often uncover this at the cheapest level with moderate reliability. On FTDNA, I have 51 matches to my own Y-DNA at a low level (25 markers). Of these 51 matches, only 12 do not match my paternal surname. There is only one that is an actual close match with 67/67 markers shared. This becomes more complicated if the paternal surname is uncommon, with very few descendants having tested, but when the alternative is not knowing anything then it seems like an easy decision to me.

My husband’s surname is Wright. He has no y-DNA matches with that surname, and only 6 matches in total. 

My father has hundreds of matches, most of them very low level matches - none have remotely similar surnames.

Hey, that's how it goes 

Really it comes down to relying on a large network of people in a shared group to have tested. If the surnames in question come from a highly divergent group you might not see naming patterns. I stand by my original sentiment though where I would rather test and find out what the match pool looks like instead of not know at all.

Do you mean that the man alleged to be her grandfather is actually her father? Would the birth mother be the wife of the "grandfather" or a woman from a younger generation? It could be possible to figure out but will require a lot of people testing and some luck. A little more information is needed for me to be clear.

Look at her alleged birth mother. Can you find other people who have had their DNA tested that match to any common ancestors in this line? Can you track down descendants of the alleged birth mother and persuade them to test? If you find matches to this maternal line, what about the alleged grandfather's wife's line? Negative results are not very informative but they can help.

It should also be possible to see the difference in numbers, but this will require some luck and a lot of descendant testing to be sure. Though until I can be clear on the scenario it is hard to say what to look for.

There's a difference between using Y-DNA testing to find close paternal matches and using this type of test to determine a paternal surname. The former is much harder and, as people have said, can require a long-term investment and some luck. If, however, you just want to determine a paternal surname, a Y-DNA test can often uncover this at the cheapest level with moderate reliability. On FTDNA, I have 51 matches to my own Y-DNA at a low level (25 markers). Of these 51 matches, only 12 do not match my paternal surname. There is only one that is an actual close match with 67/67 markers shared. This becomes more complicated if the paternal surname is uncommon, with very few descendants having tested, but when the alternative is not knowing anything then it seems like an easy decision to me.