You might want to check out the Guild of One Name Studies website at http://one-name.org/.Plenty
of advice there.
I do a one-name study of surnames of the form Kin*man (so Kingsman, Kinman etc). A simple measure is how many of them were there on the 1881 UK census (you could use the US census instead). A query on ancestry says there were 1,289 entries for Kin*man that year
There were 8,567 MacKenzies, 22,944 McKenzies and 3,819 Menzies.
As I spend about 4-5 hours mots days on my Kin*man ONS and estimate that I will never complete it, I'd suggest that you enlist some help to tackle a M*enzie ONS. wikitree would be a great way of doing a collaborative project like that.