Traditionally, hin is the word used to mean "your." The spelling him appears in one of Alduin's lines:
"Meyye! Tahrodiis aanne! Him hinde pah liiv! Zu'u hin daan!"
Do you think this is a typo, or is there perhaps some grammar behind it? Hin is used in the very next sentence, so unless the script wasn't proofread at all, this would seem strange. On the other hand, this line features three typos (aanne should be aarre "slaves," hinde should be hindde "wishes," him should be hin), so it's entirely possible. I can find no other occurences of him.
The main reason I think grammar might have a hand is because hin hindde wouldn't be the most graceful to pronounce, so perhaps hin becomes him similar to how "a" because "an" before a word with a vowel. In this case the rule seems harder to define; the next word must begin with a vowel or approximate consonant ("h," "r," or "y") and it's first syllable must end with "n." Thus we might get:
- Him hun "your hero" (vs. hin hun)
- Him in "your master" (vs. hin in)
- Him rein "your roar" (vs. hin rein)
- Him hahnu "your dream" (vs. hin hahnu)
- Him hungaar zahrahmiik "your heroic sacrifice" (vs. hin hungaar zahrahmiik)