What are all the rumors villagers can spread about you and what do they mean?

When I talk to a villager in town, sometimes they say something like

Oh! Rumor has it you're a bell pincher!

Or when your visiting a dream town a villager will say

The mayor here is such a time traveler!

I was wondering what all the rumors about your character are and what they mean. I know some like being called a Bell Pincher (you don't spend much and you have tons of money) or being called a Time Traveler (you change the clock settings a lot). But recently I've been called a "Hometown Hero" and I have no idea what that means.

So what are all the rumors that can spread around you, and what do they mean?

Solution 1:

This page has a list of all the rumors in New Leaf and how you get them (scroll down to the New Leaf section to see them): https://animalcrossing.fandom.com/wiki/Reputation

Specially, the hometown hero one you mentioned is from having a high approval rating.