whoes heads are who

[mdroberts18]

having come across a number of Greek and roman copies of Greek sculptured heads that are claimed as particular personalities but do not seem convincing i wonder if anybody knows how such ancient heads are attested if they do not have a name on them.The particular head that made me wonder is of Lysemachus the Hellenistic king of Thrace who seems to have two busts which look nothing like each other.I have seen roman emperors with names on the bust itself but most of these sculptures do not have such a name so how is it decided who they are .Looking forward to hearing suggestions
mike