As for names and titles:
The imperial family was hugely fueled by propaganda, especially by flaunting their pedigrees. This is perhaps most apparent in the Julio-Claudian period. The first tie they tended to claim was of course to Augustus Caesar, first emperor and son of the hero, Julius Caesar. This name was kept through many generations. Next, it was common to take on the name of a relative who was particularly well loved by the people. An example would be Germanicus, nephew of Tiberius and a famous general whose death was thought conspiratorial. Often in a case like that, an emperor used the name of some character "beloved by the people" to distance himself from a previous ruler who was disliked, and to strengthen ties to a certain branch of the family for many such reasons. If you look at period coinage you can see how their extended names are given to highlight relations and all. E.g. Tiberius Claudius Caesar Augustus Germanicus, was the name of Emperor Claudius, conqueror of Britain. On that note, names also were taken and given to boast of military conquest, like Germanicus (Germania) and Claudius' son, (Brittanicus).
So you see, they chose most names for themselves.
Titles? If you mean this as in political positions such as consul or imperator, then these were simply taken at the emperors will, offered by the senate to honour him, or given to another person to honor them. The emperor often naturally favoured those he liked, not always those who deserved it. Yes, a glorious military achievement might encourage an honour to be bestowed on you, but these things were often tools of flattery and boasting at the ruler's whim. A wiser man like Augustus might choose not to accept some titles and honours to show humility, and also not boast of and openly exercise the ones he possessed, so as not to intimidate the senate.
The same as with titles, heir adoption usually had little to do with giving a capable person a chance, but as a tool to tie oneself to a family, or to favour their fond ones. Claudius was even manipulated by his wife, Agrippina, to get her son from a previous marriage, Nero, in line for the throne. It's all pretty nasty and corrupt business.
