Sr,Jr,II,III, etc.
Sparteye is pretty much correct. Sr. and Jr. are father and son, Thurston Howell II would have the same name as another progenitor, usually an uncle, and III, IV, etc. follow Jr. So John Howell Sr. (who has a brother Thurston) has 2 sons, John Howell Jr. and Thurston Howell II; John Jr. has a son John Howell III, etc. As to whether Sr. or Jr. is dropped when both are no longer living, this depends on the individuals. I have known men who were Jrs. who dropped it when their father died, and have known others who have kept it, usually for professional reasons or because they have been known by that name so long they perceive a problem with dropping the Jr.
This brings up an interesting and vaguely-related subject, that of women's married names. The usual practice of a woman taking her husband's name on marriage had, traditionally, some complicated rules in etiquette, if not in law. It was formerly de rigueure to refer formally to Mary Jones, nee Doe, as Mrs. John Jones, even when she became a widow; friends could, of course, refer to her as Mary Jones, but referring to her as Mrs. Mary Jones was not considered correct. If she were divorced, however, there was a convention, not much adopted, to use the name Mrs. Doe Jones (her maiden name and husband's name).
Nowadays, there is the hyphenation system which was taken, probably, from England where it had special usages in regard to inheritances, I believe. So when John Jones marries Mary Doe, she may become Mary Doe-Jones. If John is a liberated male, he may also change his name so they both have the same name and they become John and Mary Doe-Jones. Their children usually don't take this name, however, but take the father's name. (Imagine if Algernon Doe-Jones married Maryellen Stephenson-Katzenellenbogen-- would they become Algernon and Maryellen Doe-Jones-Stephenson-Katzenellebogen?) Where would this end?
Then there is a growing tendency for women to retain their maiden names after marriage, so you have John Smith and Mary Jones as a married couple, with little Freddie and Suzie Smith. I remarked to my wife (a Registered Nurse) once that there seemed to be an unusual number of couples in our church who kept their own names and mentioned some instances. She recognized the fact that the women were physicians and explained that a physician is forbidden by law to change his/her name. Whatever name you have when you receive your MD diploma and license, you have to keep, even in the case of a woman who marries subsequently. Worse is the situation of a woman who was married and using her husband's name at the time she qualified and later is divorced -- she has to keep her former husband's name, even if she remarries.
