This is driving me crazy. What should they be called here?

"The Allies, otherwise known as the Allied Forces or the Allied Nations..."

Allied has been used casually throughout the games as well, though. When hovering over their campaign icon in RA2 is says "Play the Allied Story Campaign."

Both are right depending on grammatical usage, if without any noun and standing on its own I usually just say Allies and if with a noun it becomes Allied (Allied missions, Allied campaign)..

And now there's Red Alert 3's 'Empire of the Rising Sun'. They have several ways they can be referred to as:

1. Empire of the Rising Sun
2. Empire
3. Imperial
4. Rising Sun
5. Japan(ese)

I opted for Imperial for now, since that's what the wikia uses to group the missions. They can be changed back in a heartbeat.