It didn't actually change from Stoakes to Stokes -- it just sort of settled on one spelling. Mostly.
I'd be interested in seeing the actual sources that the name is coming from -- my bet is that the name will show up with both spellings, going on back.
The entire idea of correct spelling didn't even exist, in English, until the 18th C. And it took a while to catch on.
Before that, words were simply spelled the way they sounded, which meant that sometimes they can be found with several spellings, at the same time.
Names tended to sort of settle down about the time that you see the name change in the line you posted -- looking through it, it is given as Stoakes before William, as far back as it exists in Geni.
but that doesn't mean it shows up as Stoakes in the records. The profile managers may have made it the same -- people do that all the time -- or they may have found the information in records that "normalized" the name.
I searched both Stoakes and Stokes on geni, to see if there was a pattern, and BOTH spellings show up in profiles going back to the middle ages -- 13th and 14th century -- and the two different spellings are used in the same families.
My own last name shows up, in the earliest records we've got -- late 18th Century -- as Branan and Brannan, and then, within about 50 years, Brannen -- but all three spellings get used until about the end of the 19th Century.
I have the book that I used to upload all the information on the tree, it has several pages of notes and stories about the family which i have not yey uploaded, I will see if there is any clues in there. The book also has a number of old recipies, I will endeavour to digitise them all and upload as documents so people can copy them