🔼The name Izrahite in the Bible
The name Izrahite is curious because it doesn't really exist. The Hebrew text speaks of שמהות היזרח (Shamhuth the Izrah) and scholars suppose that the author meant to say שמהות הזרחי (Shamhuth the Zerahite), comparable to the ethnonym mentioned in verses 27:11 and 27:13.
🔼Etymology of the name Izrahite
The name Izrah(ite) is almost impossible to explain. The definite article ה would demand a noun to follow, but the word יזרח is the active form of the verb זרח (zarah), meaning to rise or shine:
Really the only way to get away with this name without reverting to the assumption of text errors and sleepy scribes, is to assume that יזרח (izrah) isn't really a name but rather a title of some sort, meaning He Will Shine, or He Shines. With the definite article: היזרח would mean The He-Will-Shine.