What's the name of the lamp that illuminates the painting in the gallery? Where can I buy it?

That's called spotlight, which is mainly used in accent lighting. Many galleries generally use cold spotlights, which will not produce thermal radiation to the irradiated objects, ensuring that the products will not be harmed, and the spotlights have good color rendering, which can make the paintings bright and beautiful. Many people who do lighting have spotlights, such as brand products, such as Opal lighting, which is better. You can visit official website or buy them at their flagship stores in Tmall and JD.COM. It's best to buy genuine products with good quality.