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.
A substantial part of the US population isn't going to know where the Ivory coast is, even less so if you call it Côte d’Ivoire, or why you're saying it in French.
Would they be better with a different country though? To be fair, a substantial part of the US population couldn’t point Iran or Ukraine[1] on the map.
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...
[2]: https://www.state.gov/countries-areas/cote-divoire