We see that in most of the Bible, the Jews are called "בני ישראל/Israelites"; only in later books are they called "יהודים/Jews" (e.g. Esther 2:5, Zechariah 8:23), after the loss of the 10 tribes. However, the only word appearing for the language of the Jews is "יהודית/Jewish/Yiddish" -- no "לשון הקדש" or "עברית". Granted, one reference is during the 2nd Temple period (Nehemiah 13:24). However, in II Kings 18:26, an Assyrian emissary is asked to speak in "יהודית" rather than in ארמית/Aramaic.
Why, then, even at this earlier point, when the entire nation of Israel lived in the land, is the language specifically referred to as the Judean language? Is that meant to imply that the other tribes were speaking something different? Or was it just the common, understood way of referring to the language?
On a related note, when did Hebrew begin to be known as עברית/Hebrew?