Unlike Reisen, Tewi's title of "Inaba" is assigned Kanji characters, which refer to the old Inaba Province in the Kansai era. "The White Hare of Inaba" is mentioned in the Kojiki.
It is said that ordinary animals who live a long time may develop profound magical abilities. Tewi is one of them.
The "wi" (ゐ) in Tewi is a hiragana that was removed from official Japanese language use by the post-war government in 1954. In present day Japanese, her name is pronounced "Tei" with an い instead of ゐ. The hiragana "wi" (ゐ) is still used artistically or stylistically as it is here in the case of Tewi (or cf. Nikka Brand Whiskey "ニッカウヰスキー"), and is similar to "thy" or "thou" in English: recognizable and still used, but almost never for official documents. Additionally, since she's at least 1300 years old, she would have received her name centuries before "wi" (ゐ) was legislated out of official use by the government.