After a while, villagers will want to give you a nickname of some sort

the nickname given seems to depend on their personality from what I've seen.
Ribbot, a jock villager, wanted to call me beefcake (or something very similar) but I said no to that XD
Later on, my sheep villager Eunice wanted to call me lamb, and now everyone in the village is calling me lamb.
One of my villagers also gave my boyfriend's character the nickname 'cupcake', which we both thought was really amusing.
So it's just a cute thing that villagers like to do :3