The change in the given names from "AA Smith" to "AB Smith" would mean that person starts a new line. of I-II-III, etc. The full name has to be exactly the same to continue the line of numbers.
Also on the topic, the use of Jr. and Sr. in public records is really unfortunate because those terms are really only used during the lifetime of the individuals concerned.
But public records obviously are meant to define identity for many years to come. When "AA Smith Sr" dies, "AA Smith Jr" becomes "Sr" (if there is also a later one so named). Or just "AA Smith" if not. Using "AA Smith I" and "AA Smith II" would have been preferable.