Change language name based on the domain i'm on
You are looking for url/domain language negociation + url/path language negociation, right ?
You need both of domain+path in /admin/config/regional/language/detection/url to determine wich language to display.

I think you have to implement a new LanguageNegociation plugin in a module which do this. Have a look at :

core/modules/language/src/Plugin/LanguageNegotiation/LanguageNegotiationUrl.php

You should be able to get your own detector (quiet looking like LanguageNegotiationUrl with both domain+path) by extending LanguageNegotiationMethodBase.