There is "Convention" or "Style" and then there is what people do. Sometimes people don't follow convention or style, either out of a personal decision, or out of ignorance.
As for Junior and Senior, in the U.S. it is not customary convention for a Junior to become a Senior in naming "when the elder man dies." It may be a form of address, i.e. a nickname, or it may be used to avoid confusion, and sometimes this makes it into the public record - but it is not the standard convention. The use of Junior, II, III, IV and so on is applied to descendents who share the *exact* same full name as their predecessor, with the style "II" usually applied when a generation is skipped in naming, or when the individual is named for someone not in direct line (i.e. after an uncle). With the disdain many modern men have for being called "Junior," the use of "II" has become increasing common as a replacement for "Jr." The style "Senior" is not applied until a like-named child is born, and is often only maintained if the child lives into adulthood.
I think it's important to stick with convention, as it is intended, for a guideline. With the exception of "Sr.," our standard shoud be name at birth. However, naming is not as tidy in reality as convention would dictate, so we have to be prepared for some individuals who will not fit into such a tidy box. If a person lives with, and dies with, a name that is unconventional I think an explanation can and should be included in the Biography section of the profile. As in "John Doe was born with the appellation 'Jr.' but became known as John Doe Sr. after his father died, and was buried with this name. He named his son 'John Doe, Jr.' as well."
Dates become very important to help distinguish between individuals, even if it's just a "born before" or "died after" year.
In any case, it's an unfortunate but common difficulty in genealogy when people don't stick with the name they are born with throughout their life, and records are often generated over time with multiple names and appellations.
To answer your specific Question: When merging, I'd choose the birth name (i.e. "Jr."), or if you don't have documentation for the birth name, whichever name has the strongest documentation, and again... note the discrepancy in the Bio.
That's my two cents.