Many streets for several countries have multiple names*. Personally, I think it's better to handle all of them instead of one (assuming there is no collision in the name) Some proggy such as NNG have option allowing to use street number instead of name for area outside your region. Unfortunately, Garmin isn't well known for having that sort of options.

* One reason is that a street might started out with one basic name (State Highway XXX), then later the city decided to renamed it to someone name to honored that person.