Time, patience and space are the key.
When a greyhound moves to a domestic home, it leaves behind it everything it has known since birth. Everyone it loved anjd everything familiar to it, so no matter how well socialised it is there is going to be a period of adjustment.
For some dogs the process is reasonably quick and incident free but for others it is a balance of time, love and support as the dog adjusts to its new life. This is a definite balancing act, as the new owner wants to give love and care but they need to be aware of not overwhelming the dog in the initial days and weeks.
So when you bring your newly adopted greyhound home, the best advice is not to panic. You have made a great decision, so park the expectations and let the dog settle in its own time. Let it come to terms with its new life, the fact that there are no more moves and 'this is its forever home'.
To avoid confusing your dog, start as you intend to finish and gently establish routines and structures as early as practical. Gradually the dog's true personality will shine through and its confidence levels will increase as the weeks and months pass.