How do you name a Jr vs II vs III?

If your name is John Henry Doe and you name your son John Henry Doe, you then become Senior (Sr.) and your son Junior (Jr.), not the second (II). If your son John Henry Doe, Jr. names his son (your grandson) the same, his son then becomes 'the third"', i.e. John Henry Doe III. However, if you name your son Richard Henry or John Harold, anything but John Henry Doe, but he still names his son (your grandson) after you, your grandson then becomes John Henry Doe II. Likewise if your brother Edward Charles Doe names his son after you, that child (your nephew) would also be John Henry Doe II. A 'junior" always has the same name as his father whereas "the second" is not named for his father but does have the same name as an older relative (grandfather, uncle, cousin, etc.). The 'third" is the third descendant in a family with the same name in either direct or indirect line. In everyday practice, the Sr., Jr., III are often only used when all parties are living but genealogically it is important to maintain the correct title to prevent confusion.