I think you’re right. I think it is a rubber plant. I don’t know the Latin name.

Maybe it just needs better light than it has been getting?

I agree that it is a rubber tree, Ficus elastica. There are many, many cultivars and not all will have identical characteristics. My variegated 'Tineke' has quite flexible, non-rubbery foliage :-)

Oops, there goes another rubber...oops there goes...another rubber tree plant!

In addition to the identification, let's try to get you some help, which has been short in supply from the above posters--no real fault of theirs, it's an ID thread. Yeah, it looks like a bit more light might be helpful. Not too much, rubber trees are really capable of tolerating low light, and you don't want to suddenly shock it, but bring it up to some brighter light, then brighter again. It should improve. They do like bright light, but not direct sun.

My mother kept one alive in deep shade and barely indirect light, but...well, that plant wasn't what I'd call happy.

Most of them are a bit more hoggy for soil space than a cup, so that cup won't do for long, and I don't think that has a bottom drain in it either? You'll want a nice, light well-draining mix of soil with a drain at the bottom. They hate sitting in water, so a drainless cup is a bad idea.

Here's two great articles for you to start with that'll help you out: https://www.apartmenttherapy.com/rubber-plant-our-best-tips-for-growing-and-care-237390

https://www.gardeningknowhow.com/houseplants/rubber-tree/how-to-care-for-a-rubber-tree-plant.htm

The second is more basic, but I like the first. :-) Although they can get fifty feet tall, you may certainly prune the thing regularly to limit height. My mother's? It never needed that as it never lived long enough. :-)

I hope that helps past just the simple ID.

Thanks guys! Will definitely give it some more light then and hopefully get it back to its best! I have it in a plastic pot with drainage holes, which is sitting inside the ceramic pot anyway so should be okay for that hopefully 😊

Thanks for all the advice!