Botanical name is Lycium barbarum. It's a shrub, but when grown as a vegetable is continually cut at ground level to provide tender young shoots. In China both fruit and leaves are believed to have a wide range of medicinal properties.

I have tried growing it from a bunch I bought at Harris Farm Market, Broadway (where it's generally available among the Chinese greens). Cuttings rooted readily enough but the plants languished with me, probably not enough attention.

Searching on a Chinese name may be unsuccessful because there are so many ways of transliterating them. Try searching on Lycium barbarum and you'll get lots of hits, including the link below.

Here is a link that might be useful: Lycium barbarum

The photos from the link don't match the plant I've seen. I have a photo I could send.

Chinese wolfberry does not have rounded leaves. You might check your spelling &/or post a picture.