This is the first and often the most contentious issue in any place branding project.
Sometimes it is simple to define the area that you are branding - a city or town for example, or a whole borough. And sometimes the boundaries of that place will match those of your local authority. That is the most straightforward scenario. But often things are more complicated.
Often, the areas defined by local government boundaries, and the names they are given, do not match the way that local people describe or recognise the places in which they live. Often business communities will perceive and describe places in a different way to residents. Sometimes the most effective place-branding work can be focused on sub areas or individual town centres within a larger place, but in such projects, one can run the risk of being seen to promote one local area above another, so local politics will need to be managed.
There are no simple answers to this and there is likely to be much debate amongst stakeholders about the best approach, especially if the area you are trying to brand cuts across local authority boundaries.
The best way to resolve this is to ensure that everyone remains focused on the strategic objectives of a project. A place brand driven chiefly by an inward investment agenda may define place differently, perhaps at a sub-regional level, than one driven by tourism, which might focus on individual destinations under a unifying county brand. If you are aiming to drive civic pride then you should define your place in the same terms as do the people who live there.
There is no reason why, over time, you cannot develop a linked portfolio of brands to encompass all of these things but at the beginning, focusing on the primary objectives of the projects will mean that defining place becomes much easier. Try not to create something that ticks everybody's boxes, and doing everything at once.