Baerdog's name is Garuik. You can find him since 0.45 update at New Road while maintaining the road during 22:00 – 6:00 Also, you can invite him to your house once during 22.00 - 00.00 in 0.49 update. (If you have invited him but you come home later than 00.00, the event will trigger in the next night at the same time in your house.)
And his content is written by guest writer Urso, so you need to wait for it like another guest writer characters.