I feel like, as someone who can read Japanese, I can add a bit to here.
I mean, I assume the Japanese versions of the games aren't titled in English.
The original games, Red and Green, are titled "Aka" and "Midori" in Japanese, but in their Kanji form, 赤 and 緑. They mean literally, and respectively, Red and Green. Pokemon Yellow wasn't titled "Yellow" in Japanese, but rather ピカチュウ, which literally is pronounced as Pikachu. Source
Why does Japan have Green (instead of Blue)
Like Steph said, Japan does have Blue. Blue/青 was the "upper-version" to Red and Green, similarly to how we have Platinum for Gen 4. Source If you think about it, we don't have a fixed gen 1; we just have Pikachu edition.
if the legendary birds are the mascot Pokemon (at least I think they are), and Articuno is clearly blue.
Box legendries didn't become a thing until Gen 2. The mascots are the starter Pokemon.
I don't know why Steph's answer says blue and green are interchangeable; this is false. Blue in Japanese is Ao/Aoi, while Green is Midori. Midori can also mean forest, though. You can't really get those mixed up, even if you tried.
In conclusion, the games have nothing to do with the birds, and they're translated to Red and Green because the Japanese they used in particular reads, specially in terms of colours, Red and Green.
It's presumed they changed Red and Green to Red and Blue to appeal to Americans