The only word I know of relevance here is toponym, one meaning of which is "a place-name".
As to the list of suffixes, I think you’d need to chase down individual meanings, unless there’s a list out there on the Internet already.
By the way, I think -burg just means "town", as in Johannesburg, "Johannes’ Town" - it’s related to the word borough. The Germanic suffix -berg is commonly applied to hills and mountains.
Of your others, most are "town" or "village" words, of varying linguistic origins.
-ton = town (English)
-ville = town (French)
-by = village (Norse)
-burg/-bury = fortress town (Germanic)
-cester = town, originally a Roman camp (Latin castra)
-ham = village, as in hamlet (French)
A shire is a district with some sort of local governor (Old English)
Toponym is also used to mean "a name given to a person or thing marking a place of origin". Denim, for instance, is a toponym by this usage, since the name derives from the French serge de Nîmes, indicating a type of serge originally manufactured in the town of Nîmes.
My favourite unexpected toponym (in this sense) is coach, named for the Hungarian town of Kocs, where various kind of horse-drawn carriage were manufactured.
Grant
PS (Added after a little thought.) The governor of the shire was the sheriff, originally the shire reeve.