Just to clarify, the order that determines what common name is shown to a user is as follows:
1 - Any name set to explictly be used in a place that the user has specified they want names to be displayed from
2 - If the user has not specified a place priority for their names, the primary name entered in the language the user is running the site in
3 - If there is no name entered in the language the user is running, the default overall taxon name, which is usually the American English one.
One of the site developers will have to answer what happens if more than 1 name is specified to be used in the same place. For instance if someone set both ‘Canada Jay’ and ‘Grey Jay’ to be used in Canada for Perisoreus canadensis. Since there is still a prioritization within that list, I assume that would drive the display (ie which ever was set as the priority name within Canada), and secondly is there any difference in behaviour if multiple names are set within a place if they are in different lexicons.