It kinda looks like a Gardenia. Are the leaves stiff? Does your pot have drainage holes? How often do you water?

Gardenia, definitely. They are much easier outside than indoors btw. Indoors, they will take full, southern sun if protected by a very light curtain otherwise east or west exposure. They like their watering, and I have been known to keep them in saucers filled with a bit of water (I can hear the protests regarding that one, but my gardenia flowers beg to differ). Winter is the real problem indoors, they hate the hot, dry heat. Keeping them as cool as possible in Winter is beneficial. Don't think of them as tropical hothouse plants...there are even species of them that overwinter outside here in New Jersey.

Thanks for the replies.

Here's a better picture.

I googled Gardenia and all the images came back as having flowers. This plant has never had flowers.

There are no drainage holes in the pot. I water it enough to keep the soil moist.

Coming up to September in Winnipeg, Canada. I don't think outdoors is an option right now unfortunately.

As far as how to take care of it going forward, it sounds like more sun and more water are in order.

Sound right?

Also some of those big stems have almost no leaves on them.
(The tallest one just has those two). Is that normal?

It definitely needs to be repotted in a pot with drainage. And put in the sunniest window you have.

The white crust around the top is some kind of build-up of salts, lime, combo of that kind of thing. I'd repot also, into a pot with a hole in the bottom so excess water can escape and not cause the roots to rot.