有名 Famous, or infamous use for celebrities, political figures, historical figure, good and bad 著名 Very famous, (not infamous) use for celebrities, political figures, historical figures, historical science figures, implies a sense of "good" too. eg Sir Issac Newton, celebrities

有名 means something is well known by people but the reason is unclear. 著名 implies that the thing you describe with this word is very significant and outstanding in some ways so people know it.

有名 = well known 著名 = famous