It's the crossroads between language, politics and identity.
This is a matter of politics and identity more than linguistics.
POLITICALLY, if a country wants to call the standards of Serbo-Croatian (that's the term linguists use, we don't use it with political intentions) different names, so be it! It's a country's prerogative to call it as such. Language is closely intertwined with cultural and social identity. If a country wants to trace its own identity by means of renaming and standardizing their dialect, it's that country's prerogative.
Linguistically speaking, that's a different matter. Serbo-Croatian is a pluricentric language meaning it has multiple standardized variants - Serbian, Croatian, Montenegrin and Bosnian (and yes that's what linguists call it, I know that name has heavy political implications, but it refers to the entire linguistic continuum). Each of them have their own governing body that standardizes each of them. So, in linguistic terms it's 1 language with multiple standards just like English and how it has an American, British, Australian, etc standard variants.
The key issue here is politics not linguistics, IMO
Personally, if USA and other Anglophone countries decide to call our/their variants of English different names, I would be cool with it. It's all politics and it's nice to formalize some sort of independent linguistic identity. Though, at the end of the day, it wouldn't matter. The linguistic differences already exist regardless of the naming change. If that were to happen, I could say that I speak more languages
. USA will then proudly speak American and understand British, Australian among other languages