I have some bad news on the matter: the way your embassy looks like in CoW is randomly chosen by the game, which means that you have no option to change that. Even more, your embassy might look different (dome, square or house-like type) from one ally to another, at least for now (hopefully a patch of the game will change this).
Still, you can change the way the flag looks like and personalize the embassy this way. Here is how to change the flag of the embassy in City of Wonder:
– click the blue “More” button in the top left corner, beneath your population
– click the red flag icon and choose any flag you want from the list (it’s free to change it, but you need to be of certain level in order to unlock more)
Hope this helps and you will feel more that you have an embassy of your own!