Cross-border town naming

Cross-border town naming occurs where towns or villages with the same or equivalent names are divided between two different countries. This does not necessarily imply that those towns or villages are located in geographic proximity or that they are located near a current border (divided cities). Reasons for this taking place may include the following:
Most places are in Europe, but there are also some examples in North America and Asia. In Europe, until the first half of the 20th century and again since the Schengen Agreement in the late 20th century, such divisions could be mostly ignored by the inhabitants.
Examples.
Note that this list includes only places with similar names that are in someway connected (by history, geography or otherwise) across modern-day international borders. Towns that have the same name but bear no relationship to each other are also very common but not particularly notable.
Europe.
Germany–Poland.
"(*) In some cases there have been added exonyms to show the relationship between the towns more clearly for people not familiar with the respective languages."
Germany–Czech Republic.
"(*) In some cases there have been added exonyms to show the relationship between the towns more clearly for people not familiar with the respective languages."
Czech Republic–Poland.
"(*) In some cases there have been added exonyms to show the relationship between the towns more clearly for people not familiar with the respective languages."
North America.
Towns and cities listed have names of a common origin across an international boundary; matching pairs across provincial or state boundaries (such as Kansas City or Lloydminster) are common but are not listed here.