Occupancy seems like the natural word for what you ask, per oxforddictionaries:
the proportion of accommodations occupied or in use
(Edit: The most applicable sense of it in wiktionary is
The act of occupying, the state of being occupied or the state of being an occupant or tenant
which is rather less satisfactory than the definition shown first.)
Here are some other possibilities: population, headcount, crowd size, census, number, complement, company, fraction. A rarely used term is filledness. Of all these, headcount perhaps fits best into your example, but others fit with minor rewording:
The elevator's headcount is six at the moment.
Those in the elevator number six at the moment.
Those in the elevator are six in number.
The elevator party is six in number.
There are six persons in the elevator.
Comment: As the last of those examples illustrates, one doesn't need a special word (besides in) and you may need to revise your question if that being so is unacceptable for some reason.
Best Answer
If you want a word that matches up with capacity, you can use occupancy for this. Per the OED: