A solid reputation works like armor. One rumor bounces off when a hundred people already know better.

Reputation is built slowly and works as a buffer when something goes wrong. If a hundred people already hold their own evidence about you, a single rumour has to fight all of it and usually loses. Without that history, one story is the only information available and becomes the truth by default.

The ordinary reliable things are what build it: turning up, doing what you said, admitting mistakes early. None of them look like reputation management at the time. That is exactly why they hold when you eventually need them to.