In our case we bougt a company in poland, while the parent company was mainly active in Germany, Austria, Switzerland. The polish company was only focussed on the polsih market, but had good skills with a cultural fit.
From my perspective it´s part of the change management to explain the “why” and this will be found in your identified synergie areas (Commercial synergies, delivery, etc).
(Communication) Techniques were: our quarterly meetings are now in english. In the beginning a little bit strange, but it makes even the buyer side feel more international.
But nevertheless, the strategy needs to fit to your aquired company. Many strategies and tactics might help.