Rosh Hashanah vs. The Sun Blessing

The Rosh Hashanah Machzor says היום הרת עולם and depending on your edition, probably translates it something like “today is the birthday of the world” or some fairly similar translation. But… Says who? This holiday is not called “Rosh Hashanah” (“start of year” or more colloquially, “new year”) in the Torah. It’s called a יום…