Ministry of war? No! Ministry of Peace!

...well... no, there isn't a need to call it that. You pretty much said it yourself.

A rose by any other name...

Right, but there's no need to call a daffodil a rose, is there? That's because it actually isn't one.

Hegemony literally requires a single state by its own definition. The word you're looking for is coalition which, indeed, isn't necessarily imperialism.

Shocking that Russia would see encroaching Western hegemony as a threat to its own.