That should not be the case at all. Do you mean renown as in something that you earn by winning battles, creating titles, hosting events etc. or do you mean the resource needed to buy legacies?
The second one would make more sense.
If you play an official character you usually start as part of a larger dynasty, f.e. Clan Ventrue. All the other Ventrue contribute to the legacy and thus it goes up over time even if you do nothing. In order to earn legacies yourself you should build special buildings, usually in duchy capitals.