My theory is years ago people did not know how to write. So, when they learned how to write their names they wrote it as it sounded according to the region they lived in.
Also, keep in mind when Daniel Webster wrote his dictionary it was no longer English as the people from England pronounced words it became American English.
My Carrol family was from VA in the 1700's. In 1850's the next generations were then living in Indiana. Part of this group moved to Illinois, they changed their spelling from Carrol to Carrell. Now we call all they Carrell's in our family the Illinois Carrell's. I t may have been intentional to change the spelling.
Hope there is some information you can gleen from this message that helps answer your Carroll vs Carrell spelling.