Serrano? That's my guess. Take a bite of one (near the top, not the bottom), if it is just mildly hot, I'd say serrano. It looks like the plant is too small to be producing fruit, so it's probably better to remove the pepper(s) until it grows to 2 foot or so, chuck

Could be a hundred different things. Do you at least have some options that you know you planted? I don't think it looks like a Serrano. Is it even full grown or still growing (size-wise)?

Its not Full Grown. The plant was purchased at a garden center outside of a grocery store. The label was missing. She bought it because it was half price since the label was missing.

The plastic pot says hierloom.

Let it ripen and let us know the color changes that will help in finding out what it is.

Well, my guess would be Cayenne.