I can think of only a few verbs like exist and belong that never take ordinary nouns as object complements. (see below)
We never say things like, *She exists a doctor. Rather, we would say, She exists as a doctor (S+V+pp)
However, we might see an infinitive functioning as an object complement as in, "She exists to heal others". She exists to do something - to heal functions as an object complement. But the infinitive is also quite verbal and could be understood as a clause - she exists, so she can heal others. This is not really about existence per se, but rather the purpose of her existence, and hence this complement phrase really produces a different meaning for the verb. We could simply say, She exists because exist does not require a complement to have complete meaning.
Belong is a little different because it is incomplete, particularly in a bare sentence. Without sufficient context, say, in answer to the question, 'do you belong?' we would rarely if ever just say, 'I belong.' Nor would we say, 'it belongs.' We normally complement this verb with a prepositional phrase or adverb phrase. I belong here, it belongs there, she belongs to the club, it belongs to him, and so on. And we never say things like, the wallet belongs me, or I belong club.
So, back to the original thought, are there any other verbs in English that never take an ordinary noun as a complement, and is there a term for such words?
Here are a few other candidates: