Looks like Teaberry, Gaultheria procumbens. WW Here is a link that might be useful: Teaberry

Why remove the leaves? The plants love them, but I know if you're dealing with an HOA, you may not have a choice. I had bromeliads, gingers, amaryllis, crinums and philodendrons under my oaks. I planted the philodendrons by laying them up against the oak tree trunk and covering with a pile of dirt. They eventually grew up into the tree and were gorgeous. I loved not having to rake under the tree, or even fertilize much, because of the leaves. Never "planted" a bromeliad. Just laid them on the ground and let them do their thing. The gingers only need an inch of dirt over them to grow. The giant crinum was planted quite by accident when I was given one which I tossed under the tree and forgot about. It rooted into the ground, still growing on its side, and bloomed like mad every year. The amaryllis I started as tiny bulbets given to me by a friend, so I only had to dig a tiny little hole and cover with dirt to start them. They took a few years to bloom, but they did, and multiplied like mad. There is a grass that will grow under oaks. It's called "Bitter Blue" St. Augustine, and it's not that easy to find. Mine was there when I moved in, and wherever it grew out from under the shade, it died, because I didn't irrigate the lawn. Still, it thrived under the oak. Monkey grass is also easy to plant and grow under oaks, because you can pull the clumps apart and just plant the sprigs. It fills in rapidly. Same with the green or variegated ornamental sweet potato. Just root some cuttings in water and plant them as soon as they have tiny 1/2" roots on them. Of course, you can always mulch and use containers for flowers if you want. A lot of people do that.

Just be sure, whatever you choose, that you do all you can to protect the root/soil system under those oaks. The most important part of an oak's root system is extremely shallow; when we compact or cut those shallow, fibrous roots it can be very damaging. So, NO TILLING! I would recommend that you plant very young plants and just a few of them. Be prepared to water quite a bit initially.....those established trees will be very stingy with their rainfall!

"I have been reading some forums that hydrangeas can cause issues with the tree's roots so I didn't know if anyone had experience with this." All kinds of claims that are not true are made on forums. Is there any corroboration of such claims by a viable source? It's not realistic in my mind that a couple of Hydrangeas are capable, or even have a hope of, killing or harming an oak tree. But as Babs says, it's pretty dark in there. Unless you remove some of the bottom branches and let light in, I don't think you're going to get a great display. A huge part of an older tree's magnificence is its trunk. Removing lower limbs exposes this great feature.