A country picker and a formal document don't necessarily want the same name. "Netherlands" is a useful label in a dropdown. "Kingdom of the Netherlands" is the formal name. Someone viewing the country in Dutch may want "Nederland".
Instead of choosing one and making you reconstruct the others, /country/NL includes all three in the basic response. Here are the relevant fields:
{
"name": "Netherlands",
"name_full": "Kingdom of the Netherlands",
"name_local": "Nederland"
}
Use name for the usual English label. name_full is the formal English form when you need it. name_local preserves the local name when it differs from name. It is null when absent or identical. Japan's is 日本.
These fields describe different forms of the same name. They aren't a translation service, and name_local doesn't change with the reader's browser language. A country can also use the same text for more than one field, as Japan does for name and name_full.
For most interfaces, name is all you need. The formal and local names stay beside it in the basic response, so a more specific display does not require another lookup or a guess at the formal wording.