Yes, they want that; why not do that then? Like with Czechia[1], Sri Lanka, the Netherlands and others?
Côte d’Ivoire is indeed also known as "Ivory Coast"; still, you can write a sentence in English with "Côte d’Ivoire" and it doesn't raise an eyebrow[2]. If that's not enough, there's Curaçao too.
[1]: https://en.wikipedia.org/wiki/Name_of_the_Czech_Republic#Ado...