Thanks for your contribution to Parf Edhellen!
Our only attested examples of this suffix for “my” are gûr → guren and lam → lammen. Those are both derived from a word anciently ending in e: gorē, lambē. It is unclear whether a word like kambā > cam with a different final vowel would produce camman or cammen. With Tolkien’s revision of verbal noun suffix-ste >> -sta, we can’t be sure what ancient vowel eneth would have, so I would stick to i eneth nín like attested i eneth lín “your name” in the Lord’s prayer.
gilruin