The description states:
On its turn, it can move only toward its target by the most direct route, and it can use its action only to attack its target.
Who controls whether he indeed uses what he can?
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The Hound doesn't have to do it, the player decides whether the Hound moves and/or attacks.
When a creature must do something, 5e uses the must terminology, like in Death Saving throws:
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life.
Some spells also specify that the DM has their statistics and how they should behave, like Conjure Elemental.
It obeys any verbal commands that you issue to it (no action required by you). If you don't issue any commands to the elemental, it defends itself from Hostile creatures but otherwise takes no Actions. [...] The DM has the elemental's Statistics.
For Hound of Ill Omen, no such descriptions exist, thus giving you (the player) full control (with the above restrictions, of course) over the Hound.