In my Underwood family, the name's Jacob and Sidney seem to pop up a lot, including the "nickname as a name" Jake.
On the Shepherd side, these three repeat in each generation: James, Thomas, and John. The initials "T A" showed up in three successive generations, though not in a direct line.
In my Neal line: George, Alexander, and Henry predominate. In my Lawing line: William and Andrew (over and over again), and surprisingly Middleton. Kerr line: Jesse and Claiborn.
The female family members invariably received Elizabeth, Margaret, with combinations of those and their variants.
The only Sr., Jr., and III of a name was Ralph Sidney, the first being my grandfather. Interestingly, it was his wife's surname that has carried through four generations - Neal.