It's not clear by the written rules. But it's a reasonable thought.
So, as the spell is written it doesn't move at all, which begs the question, what happens if my world is on a moving planet? Will the hound instantly fly away and disappear into space?
Since that doesn't make for a functional spell at all it's quite obvious the hound is meant to stay still in relation to some frame of reference. Which is normally just the ground you are standing on.
But clearly, in D&D we sometimes have fights in places that are moving in relation to the world. Could be a carriage, a ship, or whatever. Does the hound remain stationary in relation to the ground there, meaning it's displaced from where we are standing?
I think it's a ruling many DMs would make that the hound stays anchored to the surface it was summoned in. The other answer as of now, explains this as being due to that hypothetical ship or whatnot having its own mobile 'space' (which I think refers to it having its own grid and that objects placed in it remain stationary in relation to each other).
I think this raises some issues when you have multiple representations of spaces. For instance, you could have a grid for your ship and another battle map where your ship is a miniature and other ships and creatures exist there as well. There, your hound could interact with a hostile creature next to your ship, even if it's not in the mobile space represented on your ship's grid (let's say it only goes up to the border of your ship). So we are forced to recognize the hound as moving through a space.
Ruling that the hound can remain stationary in relation to any surface it's summoned on seems quite reasonable.