Explanation #1: Rashi spells the first 'Hurmiz' with an 'Alef' (at the beginning), and the second one without one.

Explanation #2: Rabeinu spells them both without an 'Alef', only the first one he spells with a "Zayin' (at the end), which is an expression of 'a Divine Chein', and 'Ifra' is an expression of strength or B'rachah (like 'Apiryon Nimtayah', at the end of Bava Metzi'a); whereas the second one, he spells with a 'Nun' (the name of a demon, like 'Hurmin bar Lilsa', in Bava Basra 73a)

Implied Question: On what grounds was He permitted to render Himself Tamei (Kevayachol), however?

Answer: Since Yisrael are called children of Hash-m (and a Kohen is permitted to render himself Tamei for the seven relatives), it was permitted.