Well, "idem, eadem, idem" has two meanings at least:
1)"the same" as you typed,
2)but also "just this one" (hm, I don't know whether I expressed it right in English, but in Polish it means "ten właśnie"
)
The pronoun is similar to "is, ea, id", but is more stronger and more concrete/specific... This is why I have chosen it. I read the English sentence in this way: "I belong to this concrete place" or "I belong just to this place" (I was followed by the note of the requester in he remark field)
But, of course, "eum" and "hunc" is also right.
Favorite translations
