Note: Very inexperienced with OSM.
I was looking at the Atlantic Ocean and ocean and noticed “Hamilton” is the label for Bermuda when zoomed way out. As you zoom in, the label changes to Bermuda, and as you zoom in further you can see Bermuda and Hamilton.
Why is the label for the capital of Bermuda, displayed when zoomed way out instead of Bermuda itself? Is it working correctly?
The way that labels are selected will depend on which map renderer you are using, and you haven’t said which.
However which labels get rendered will depend on what else would conflict with the display of that label.
Also different zoom levels are rendered at different times, so it is possible that there was a temporary error in the data.
If you are looking at the standard rendering, I would say that it is probably because “Bermuda” becomes too large to be contained completely within the bounds of the territorial waters of the country.
The Humanitarian rendering seems to have a different policy.
Have a look at help.openstreetmap.org for many other examples of odd choices for the automatic renderer. Virtually all of the ones people complain about are at low zoom levels.
As hadw explains it will have to do with which label is easier to render for the Mapnik engine: the actual underlying rules are complex and generally can be regarded as opaque.