Why is the place called Hati-Dunga?

You may have heard a certain place in lower Motithang being referred to as Hati-Dunga (The Elephant Rock) but have you seen it? 

I thought it was just named after a random rock that looked like an elephant 🐘 but it's not. It's named after a more prominent rock and a space around it. It doesn't look so much like an elephant if not for the colour and the eyes drawn over it but it's regarded as a place of worship by the Hindus. It may be associated with Lord Ganesh. 

The place is surprisingly so welcoming. It is developed and managed so well within a campus wall with a gate that's protected with a lock. There is a tiled footpath inside the gate to circumambulate the sacred rock. There seems to be a pujari who makes an offering every day looking at how everything is in order. 

I think the place is already quite popular among the local Hindu devotees, and I believe it can be a hotspot for Indian tourists. 

BONUS: A Little further from the sacred rock there is a magnificent blue house that's so characteristic of Southern Bhutan. But I have never seen such a massive and elegant Lhotshampa style house across the entire southern belt, let alone Thimphu. It is a Hati among the southern Bhutanese houses and for it to be next to the Hati Dunga doesn't seem like a coincidence. How are they connected?