I'm in the process of planning for a surname DNA study. A little more difficult for me to get started as the companies like familytreedna want you to purchase a kit first, and as I am female, and don't have near male relatives with the surname I am interested in (my maternal grandmother) I need to get other people on board with the idea first.
For me as a GOONS member (Guild of one-name studies), a DNA study will never replace the paper trail, but it should be able to give me some valuable clues to link together some of the separate family groups I already have a good documented history for. It can be a way to start breaking down brick walls. For example I have a number of separate family lines of SENNETTs that go back to Ireland, with immigration to the UK in the mid 1840's, many of whom claim to originate from Co Wicklow. The chances that they are brothers, or cousins is fairly good, but if I could get DNA evidence that showed exact matches between descendants of the different lines, then it would give me clearer direction for searching for those common links. In another example I have someone claiming that a very early ancestor of a cornish line may have come from Cambridgeshire, where I have trees back to about the same point in time. If DNA matched exactly there it would not only link two of the earliest family groups I have, but would give added weight to the claims that the man who came from Cambridgeshire is the same person as the purported father of the cornish ancestor - this would direct my research to how someone from Cambridgeshire came to be living in Cornwall. A third useful thing that DNA can do particularly for a one-name study is rule out family groups where the current name of SENNETT has originated from other than the irish SINNOTT/SYNNOTT or the cambridgeshire SENIGHT and has been the result of someone just taking on SENNETT as a fairly close anglicisation of for example a german or austrian name.
I'm not that keen on the "health benefits" to be obtained from 23andme - while a few of the disorders can be reasonably predicted from their testing, in most cases your family history would have thrown this up already and you be aware of inherited conditions. Most of the other "probability" of disease is not actually that much different from the general population when you look at the chances properly. I am also not particularly interested in the DNA testing that gives information on racial backgrounds (mostly mtDNA I think, or female line DNA) because again, for most folk a decent paper trail of genealogy will make that clear.
The only other thing that is stopping me from starting a surname DNA study right now is that I think a proper one-name project really needs to involve lots of different family groups. Already I link in with quite a few researchers who have well-documented their own family lines, and it would make sense to get them on board with a DNA study to both share the load of analysing and reporting, as well as identifying appropriate people to test (who will often be them or someone from their immediate family). People just doing individual testing won't get anywhere near the benefits and possible matches that people who are doing it as part of a defined surname study will. A surname study can also set up a fund with some of the DNA companies to allow other family members (eg women) to contribute to the costs of the tests, and also the tests can be bought at a considerably discount if through a formal study group.
If anyone does have SENNETT/SINNOTT/SENNITT connections and is interested in genealogical DNA, then please contact me - you can pick up my direct email address from the Guild of One Name Studies website, or start my PM'ing me here.