My thinking in them calling it the delta variant is to distance themselves from calling certain variants from different countries like they did before. Prior to the India variant, as they called it, each variant was named after the country of origin. These counties played along to gain control of their citizens. Then the India variant came along.

Queue the massive amount of Indians giving the DS backlash as the pointed out their phoney attempts to create varients out of nowhere. This hit the internet, and soon anyone with a brain knew the whole thing was a crock of shit. So, instead of repeating that disaster, they switched to the phonetic alphabet/Greek lettering as to not screw the pooch again.

We still know it's all bologna though.